{"cells": [{"cell_type": "markdown", "id": "7a37951c", "metadata": {"papermill": {"duration": 0.023386, "end_time": "2021-09-16T12:40:39.258673", "exception": false, "start_time": "2021-09-16T12:40:39.235287", "status": "completed"}, "tags": []}, "source": ["\n", "# Tutorial 7: Deep Energy-Based Generative Models\n", "\n", "* **Author:** Phillip Lippe\n", "* **License:** CC BY-SA\n", "* **Generated:** 2021-09-16T14:32:29.871712\n", "\n", "In this tutorial, we will look at energy-based deep learning models, and focus on their application as generative models.\n", "Energy models have been a popular tool before the huge deep learning hype around 2012 hit.\n", "However, in recent years, energy-based models have gained increasing attention because of improved training methods and tricks being proposed.\n", "Although they are still in a research stage, they have shown to outperform strong Generative Adversarial Networks\n", "in certain cases which have been the state of the art of generating images\n", "([blog post](https://ajolicoeur.wordpress.com/the-new-contender-to-gans-score-matching-with-langevin-sampling/)about strong energy-based models,\n", "[blog post](https://medium.com/syncedreview/nvidia-open-sources-hyper-realistic-face-generator-stylegan-f346e1a73826) about the power of GANs).\n", "Hence, it is important to be aware of energy-based models, and as the theory can be abstract sometimes,\n", "we will show the idea of energy-based models with a lot of examples.\n", "This notebook is part of a lecture series on Deep Learning at the University of Amsterdam.\n", "The full list of tutorials can be found at https://uvadlc-notebooks.rtfd.io.\n", "\n", "\n", "---\n", "Open in [{height=\"20px\" width=\"117px\"}](https://colab.research.google.com/github/PytorchLightning/lightning-tutorials/blob/publication/.notebooks/course_UvA-DL/07-deep-energy-based-generative-models.ipynb)\n", "\n", "Give us a \u2b50 [on Github](https://www.github.com/PytorchLightning/pytorch-lightning/)\n", "| Check out [the documentation](https://pytorch-lightning.readthedocs.io/en/latest/)\n", "| Join us [on Slack](https://join.slack.com/t/pytorch-lightning/shared_invite/zt-pw5v393p-qRaDgEk24~EjiZNBpSQFgQ)"]}, {"cell_type": "markdown", "id": "7f00f90d", "metadata": {"papermill": {"duration": 0.021442, "end_time": "2021-09-16T12:40:39.301749", "exception": false, "start_time": "2021-09-16T12:40:39.280307", "status": "completed"}, "tags": []}, "source": ["## Setup\n", "This notebook requires some packages besides pytorch-lightning."]}, {"cell_type": "code", "execution_count": 1, "id": "33e8ad5c", "metadata": {"colab": {}, "colab_type": "code", "execution": {"iopub.execute_input": "2021-09-16T12:40:39.347844Z", "iopub.status.busy": "2021-09-16T12:40:39.347375Z", "iopub.status.idle": "2021-09-16T12:40:39.349918Z", "shell.execute_reply": "2021-09-16T12:40:39.349436Z"}, "id": "LfrJLKPFyhsK", "lines_to_next_cell": 0, "papermill": {"duration": 0.026972, "end_time": "2021-09-16T12:40:39.350031", "exception": false, "start_time": "2021-09-16T12:40:39.323059", "status": "completed"}, "tags": []}, "outputs": [], "source": ["# ! pip install --quiet \"torchvision\" \"torch>=1.6, <1.9\" \"tensorboard\" \"matplotlib\" \"pytorch-lightning>=1.3\" \"torchmetrics>=0.3\""]}, {"cell_type": "markdown", "id": "9eea4d0b", "metadata": {"papermill": {"duration": 0.022362, "end_time": "2021-09-16T12:40:39.394135", "exception": false, "start_time": "2021-09-16T12:40:39.371773", "status": "completed"}, "tags": []}, "source": ["<div class=\"center-wrapper\"><div class=\"video-wrapper\"><iframe src=\"https://www.youtube.com/embed/E6PDwquBBQc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe></div></div>\n", "First, let's import our standard libraries below."]}, {"cell_type": "code", "execution_count": 2, "id": "8882a3d0", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:39.460040Z", "iopub.status.busy": "2021-09-16T12:40:39.459550Z", "iopub.status.idle": "2021-09-16T12:40:40.727064Z", "shell.execute_reply": "2021-09-16T12:40:40.726625Z"}, "papermill": {"duration": 1.298062, "end_time": "2021-09-16T12:40:40.727182", "exception": false, "start_time": "2021-09-16T12:40:39.429120", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["/tmp/ipykernel_1940/3480345581.py:30: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n", " set_matplotlib_formats(\"svg\", \"pdf\") # For export\n", "Global seed set to 42\n"]}], "source": ["# Standard libraries\n", "import os\n", "import random\n", "import urllib.request\n", "from urllib.error import HTTPError\n", "\n", "# Plotting\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# PyTorch Lightning\n", "import pytorch_lightning as pl\n", "\n", "# PyTorch\n", "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "import torch.utils.data as data\n", "\n", "# Torchvision\n", "import torchvision\n", "\n", "# %matplotlib inline\n", "from IPython.display import set_matplotlib_formats\n", "from pytorch_lightning.callbacks import LearningRateMonitor, ModelCheckpoint\n", "from torchvision import transforms\n", "from torchvision.datasets import MNIST\n", "\n", "set_matplotlib_formats(\"svg\", \"pdf\") # For export\n", "matplotlib.rcParams[\"lines.linewidth\"] = 2.0\n", "\n", "# Path to the folder where the datasets are/should be downloaded (e.g. CIFAR10)\n", "DATASET_PATH = os.environ.get(\"PATH_DATASETS\", \"data\")\n", "# Path to the folder where the pretrained models are saved\n", "CHECKPOINT_PATH = os.environ.get(\"PATH_CHECKPOINT\", \"saved_models/tutorial8\")\n", "\n", "# Setting the seed\n", "pl.seed_everything(42)\n", "\n", "# Ensure that all operations are deterministic on GPU (if used) for reproducibility\n", "torch.backends.cudnn.determinstic = True\n", "torch.backends.cudnn.benchmark = False\n", "\n", "device = torch.device(\"cuda:0\") if torch.cuda.is_available() else torch.device(\"cpu\")"]}, {"cell_type": "markdown", "id": "8fa2ad82", "metadata": {"papermill": {"duration": 0.022316, "end_time": "2021-09-16T12:40:40.772238", "exception": false, "start_time": "2021-09-16T12:40:40.749922", "status": "completed"}, "tags": []}, "source": ["We also have pre-trained models that we download below."]}, {"cell_type": "code", "execution_count": 3, "id": "8ddb6202", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:40.823433Z", "iopub.status.busy": "2021-09-16T12:40:40.820802Z", "iopub.status.idle": "2021-09-16T12:40:41.030878Z", "shell.execute_reply": "2021-09-16T12:40:41.030402Z"}, "papermill": {"duration": 0.236743, "end_time": "2021-09-16T12:40:41.030985", "exception": false, "start_time": "2021-09-16T12:40:40.794242", "status": "completed"}, "tags": []}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Downloading https://raw.githubusercontent.com/phlippe/saved_models/main/tutorial8/MNIST.ckpt...\n", "Downloading https://raw.githubusercontent.com/phlippe/saved_models/main/tutorial8/tensorboards/events.out.tfevents.MNIST...\n"]}], "source": ["# Github URL where saved models are stored for this tutorial\n", "base_url = \"https://raw.githubusercontent.com/phlippe/saved_models/main/tutorial8/\"\n", "# Files to download\n", "pretrained_files = [\"MNIST.ckpt\", \"tensorboards/events.out.tfevents.MNIST\"]\n", "\n", "# Create checkpoint path if it doesn't exist yet\n", "os.makedirs(CHECKPOINT_PATH, exist_ok=True)\n", "\n", "# For each file, check whether it already exists. If not, try downloading it.\n", "for file_name in pretrained_files:\n", " file_path = os.path.join(CHECKPOINT_PATH, file_name)\n", " if \"/\" in file_name:\n", " os.makedirs(file_path.rsplit(\"/\", 1)[0], exist_ok=True)\n", " if not os.path.isfile(file_path):\n", " file_url = base_url + file_name\n", " print(\"Downloading %s...\" % file_url)\n", " try:\n", " urllib.request.urlretrieve(file_url, file_path)\n", " except HTTPError as e:\n", " print(\n", " \"Something went wrong. Please try to download the files manually,\"\n", " \" or contact the author with the full output including the following error:\\n\",\n", " e,\n", " )"]}, {"cell_type": "markdown", "id": "54b9725b", "metadata": {"papermill": {"duration": 0.02216, "end_time": "2021-09-16T12:40:41.075989", "exception": false, "start_time": "2021-09-16T12:40:41.053829", "status": "completed"}, "tags": []}, "source": ["## Energy Models\n", "\n", "In the first part of this tutorial, we will review the theory of the energy-based models\n", "(the same theory has been discussed in Lecture 8).\n", "While most of the previous models had the goal of classification or regression,\n", "energy-based models are motivated from a different perspective: density estimation.\n", "Given a dataset with a lot of elements, we want to estimate the probability distribution over the whole data space.\n", "As an example, if we model images from CIFAR10, our goal would be to have a probability distribution\n", "over all possible images of size $32\\times32\\times3$ where those images have a high likelihood\n", "that look realistic and are one of the 10 CIFAR classes.\n", "Simple methods like interpolation between images don't work because images are extremely high-dimensional\n", "(especially for large HD images).\n", "Hence, we turn to deep learning methods that have performed well on complex data.\n", "\n", "However, how do we predict a probability distribution $p(\\mathbf{x})$ over so many dimensions using a simple neural network?\n", "The problem is that we cannot just predict a score between 0 and 1,\n", "because a probability distribution over data needs to fulfill two properties:\n", "\n", "1.\n", "The probability distribution needs to assign any possible value of\n", "$\\mathbf{x}$ a non-negative value: $p(\\mathbf{x}) \\geq 0$.\n", "2.\n", "The probability density must sum/integrate to 1 over **all** possible inputs:\n", "$\\int_{\\mathbf{x}} p(\\mathbf{x}) d\\mathbf{x} = 1$.\n", "\n", "Luckily, there are actually many approaches for this, and one of them are energy-based models.\n", "The fundamental idea of energy-based models is that you can turn any function\n", "that predicts values larger than zero into a probability distribution by dviding by its volume.\n", "Imagine we have a neural network, which has as output a single neuron, like in regression.\n", "We can call this network $E_{\\theta}(\\mathbf{x})$, where $\\theta$ are our parameters of the network,\n", "and $\\mathbf{x}$ the input data (e.g. an image).\n", "The output of $E_{\\theta}$ is a scalar value between $-\\infty$ and $\\infty$.\n", "Now, we can use basic probability theory to *normalize* the scores of all possible inputs:\n", "\n", "$$\n", "q_{\\theta}(\\mathbf{x}) = \\frac{\\exp\\left(-E_{\\theta}(\\mathbf{x})\\right)}{Z_{\\theta}} \\hspace{5mm}\\text{where}\\hspace{5mm}\n", "Z_{\\theta} = \\begin{cases}\n", " \\int_{\\mathbf{x}}\\exp\\left(-E_{\\theta}(\\mathbf{x})\\right) d\\mathbf{x} & \\text{if }x\\text{ is continuous}\\\\\n", " \\sum_{\\mathbf{x}}\\exp\\left(-E_{\\theta}(\\mathbf{x})\\right) & \\text{if }x\\text{ is discrete}\n", "\\end{cases}\n", "$$\n", "\n", "The $\\exp$-function ensures that we assign a probability greater than zero to any possible input.\n", "We use a negative sign in front of $E$ because we call $E_{\\theta}$ to be the energy function:\n", "data points with high likelihood have a low energy, while data points with low likelihood have a high energy.\n", "$Z_{\\theta}$ is our normalization terms that ensures that the density integrates/sums to 1.\n", "We can show this by integrating over $q_{\\theta}(\\mathbf{x})$:\n", "\n", "$$\n", "\\int_{\\mathbf{x}}q_{\\theta}(\\mathbf{x})d\\mathbf{x} =\n", "\\int_{\\mathbf{x}}\\frac{\\exp\\left(-E_{\\theta}(\\mathbf{x})\\right)}{\\int_{\\mathbf{\\tilde{x}}}\\exp\\left(-E_{\\theta}(\\mathbf{\\tilde{x}})\\right) d\\mathbf{\\tilde{x}}}d\\mathbf{x} =\n", "\\frac{\\int_{\\mathbf{x}}\\exp\\left(-E_{\\theta}(\\mathbf{x})\\right)d\\mathbf{x}}{\\int_{\\mathbf{\\tilde{x}}}\\exp\\left(-E_{\\theta}(\\mathbf{\\tilde{x}})\\right) d\\mathbf{\\tilde{x}}} = 1\n", "$$\n", "\n", "Note that we call the probability distribution $q_{\\theta}(\\mathbf{x})$ because this is the learned distribution by the model,\n", "and is trained to be as close as possible to the *true*, unknown distribution $p(\\mathbf{x})$.\n", "\n", "The main benefit of this formulation of the probability distribution is its great flexibility as we can choose\n", "$E_{\\theta}$ in whatever way we like, without any constraints.\n", "Nevertheless, when looking at the equation above, we can see a fundamental issue: How do we calculate $Z_{\\theta}$?\n", "There is no chance that we can calculate $Z_{\\theta}$ analytically for high-dimensional input\n", "and/or larger neural networks, but the task requires us to know $Z_{\\theta}$.\n", "Although we can't determine the exact likelihood of a point, there exist methods with which we can train energy-based models.\n", "Thus, we will look next at \"Contrastive Divergence\" for training the model."]}, {"cell_type": "markdown", "id": "5f67ccab", "metadata": {"papermill": {"duration": 0.022199, "end_time": "2021-09-16T12:40:41.120470", "exception": false, "start_time": "2021-09-16T12:40:41.098271", "status": "completed"}, "tags": []}, "source": ["### Contrastive Divergence\n", "\n", "When we train a model on generative modeling, it is usually done by maximum likelihood estimation.\n", "In other words, we try to maximize the likelihood of the examples in the training set.\n", "As the exact likelihood of a point cannot be determined due to the unknown normalization constant $Z_{\\theta}$,\n", "we need to train energy-based models slightly different.\n", "We cannot just maximize the un-normalized probability $\\exp(-E_{\\theta}(\\mathbf{x}_{\\text{train}}))$\n", "because there is no guarantee that $Z_{\\theta}$ stays constant, or that $\\mathbf{x}_{\\text{train}}$\n", "is becoming more likely than the others.\n", "However, if we base our training on comparing the likelihood of points, we can create a stable objective.\n", "Namely, we can re-write our maximum likelihood objective where we maximize the probability\n", "of $\\mathbf{x}_{\\text{train}}$ compared to a randomly sampled data point of our model:\n", "\n", "$$\n", "\\begin{split}\n", " \\nabla_{\\theta}\\mathcal{L}_{\\text{MLE}}(\\mathbf{\\theta};p) & = -\\mathbb{E}_{p(\\mathbf{x})}\\left[\\nabla_{\\theta}\\log q_{\\theta}(\\mathbf{x})\\right]\\\\[5pt]\n", " & = \\mathbb{E}_{p(\\mathbf{x})}\\left[\\nabla_{\\theta}E_{\\theta}(\\mathbf{x})\\right] - \\mathbb{E}_{q_{\\theta}(\\mathbf{x})}\\left[\\nabla_{\\theta}E_{\\theta}(\\mathbf{x})\\right]\n", "\\end{split}\n", "$$\n", "\n", "Note that the loss is still an objective we want to minimize.\n", "Thus, we try to minimize the energy for data points from the dataset, while maximizing the energy for randomly\n", "sampled data points from our model (how we sample will be explained below).\n", "Although this objective sounds intuitive, how is it actually derived from our original distribution $q_{\\theta}(\\mathbf{x})$?\n", "The trick is that we approximate $Z_{\\theta}$ by a single Monte-Carlo sample.\n", "This gives us the exact same objective as written above.\n", "\n", "Visually, we can look at the objective as follows (figure credit\n", "- [Stefano Ermon and Aditya Grover](https://deepgenerativemodels.github.io/assets/slides/cs236_lecture11.pdf)):\n", "\n", "<center width=\"100%\"><img src=\"https://github.com/PyTorchLightning/lightning-tutorials/raw/main/course_UvA-DL/07-deep-energy-based-generative-models/contrastive_divergence.svg\" width=\"700px\"></center>\n", "\n", "$f_{\\theta}$ represents $\\exp(-E_{\\theta}(\\mathbf{x}))$ in our case.\n", "The point on the right, called \"correct answer\", represents a data point from the dataset\n", "(i.e. $x_{\\text{train}}$), and the left point, \"wrong answer\", a sample from our model (i.e. $x_{\\text{sample}}$).\n", "Thus, we try to \"pull up\" the probability of the data points in the dataset,\n", "while \"pushing down\" randomly sampled points.\n", "The two forces for pulling and pushing are in balance iff $q_{\\theta}(\\mathbf{x})=p(\\mathbf{x})$."]}, {"cell_type": "markdown", "id": "2b9dc4a8", "metadata": {"papermill": {"duration": 0.022022, "end_time": "2021-09-16T12:40:41.164700", "exception": false, "start_time": "2021-09-16T12:40:41.142678", "status": "completed"}, "tags": []}, "source": ["### Sampling from Energy-Based Models\n", "\n", "For sampling from an energy-based model, we can apply a Markov Chain Monte Carlo using Langevin Dynamics.\n", "The idea of the algorithm is to start from a random point, and slowly move towards the direction\n", "of higher probability using the gradients of $E_{\\theta}$.\n", "Nevertheless, this is not enough to fully capture the probability distribution.\n", "We need to add noise $\\omega$ at each gradient step to the current sample.\n", "Under certain conditions such as that we perform the gradient steps an infinite amount of times,\n", "we would be able to create an exact sample from our modeled distribution.\n", "However, as this is not practically possible, we usually limit the chain to $K$ steps\n", "($K$ a hyperparameter that needs to be finetuned).\n", "Overall, the sampling procedure can be summarized in the following algorithm:\n", "\n", "<center width=\"100%\" style=\"padding:15px\"><img src=\"https://github.com/PyTorchLightning/lightning-tutorials/raw/main/course_UvA-DL/07-deep-energy-based-generative-models/sampling.svg\" width=\"750px\"></center>"]}, {"cell_type": "markdown", "id": "c20bf67b", "metadata": {"papermill": {"duration": 0.02196, "end_time": "2021-09-16T12:40:41.209186", "exception": false, "start_time": "2021-09-16T12:40:41.187226", "status": "completed"}, "tags": []}, "source": ["### Applications of Energy-based models beyond generation\n", "\n", "Modeling the probability distribution for sampling new data is not the only application of energy-based models.\n", "Any application which requires us to compare two elements is much simpler to learn\n", "because we just need to go for the higher energy.\n", "A couple of examples are shown below (figure credit\n", "- [Stefano Ermon and Aditya Grover](https://deepgenerativemodels.github.io/assets/slides/cs236_lecture11.pdf)).\n", "A classification setup like object recognition or sequence labeling can be considered as an energy-based\n", "task as we just need to find the $Y$ input that minimizes the output $E(X, Y)$ (hence maximizes probability).\n", "Similarly, a popular application of energy-based models is denoising of images.\n", "Given an image $X$ with a lot of noise, we try to minimize the energy by finding the true input image $Y$.\n", "\n", "<center width=\"100%\"><img src=\"https://github.com/PyTorchLightning/lightning-tutorials/raw/main/course_UvA-DL/07-deep-energy-based-generative-models/energy_models_application.png\" width=\"600px\"></center>\n", "\n", "Nonetheless, we will focus on generative modeling here as in the next couple of lectures,\n", "we will discuss more generative deep learning approaches."]}, {"cell_type": "markdown", "id": "89370a6d", "metadata": {"papermill": {"duration": 0.022103, "end_time": "2021-09-16T12:40:41.253274", "exception": false, "start_time": "2021-09-16T12:40:41.231171", "status": "completed"}, "tags": []}, "source": ["## Image generation\n", "\n", "<div class=\"center-wrapper\"><div class=\"video-wrapper\"><iframe src=\"https://www.youtube.com/embed/QJ94zuSQoP4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe></div></div>\n", "\n", "As an example for energy-based models, we will train a model on image generation.\n", "Specifically, we will look at how we can generate MNIST digits with a very simple CNN model.\n", "However, it should be noted that energy models are not easy to train and often diverge\n", "if the hyperparameters are not well tuned.\n", "We will rely on training tricks proposed in the paper\n", "[Implicit Generation and Generalization in Energy-Based Models](https://arxiv.org/abs/1903.08689)\n", "by Yilun Du and Igor Mordatch ([blog](https://openai.com/blog/energy-based-models/)).\n", "The important part of this notebook is however to see how the theory above can actually be used in a model.\n", "\n", "### Dataset\n", "\n", "First, we can load the MNIST dataset below.\n", "Note that we need to normalize the images between -1 and 1 instead of mean 0 and std 1 because during sampling,\n", "we have to limit the input space.\n", "Scaling between -1 and 1 makes it easier to implement it."]}, {"cell_type": "code", "execution_count": 4, "id": "d20babd4", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.303522Z", "iopub.status.busy": "2021-09-16T12:40:41.302963Z", "iopub.status.idle": "2021-09-16T12:40:41.332018Z", "shell.execute_reply": "2021-09-16T12:40:41.331579Z"}, "papermill": {"duration": 0.056251, "end_time": "2021-09-16T12:40:41.332136", "exception": false, "start_time": "2021-09-16T12:40:41.275885", "status": "completed"}, "tags": []}, "outputs": [], "source": ["# Transformations applied on each image => make them a tensor and normalize between -1 and 1\n", "transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))])\n", "\n", "# Loading the training dataset. We need to split it into a training and validation part\n", "train_set = MNIST(root=DATASET_PATH, train=True, transform=transform, download=True)\n", "\n", "# Loading the test set\n", "test_set = MNIST(root=DATASET_PATH, train=False, transform=transform, download=True)\n", "\n", "# We define a set of data loaders that we can use for various purposes later.\n", "# Note that for actually training a model, we will use different data loaders\n", "# with a lower batch size.\n", "train_loader = data.DataLoader(train_set, batch_size=128, shuffle=True, drop_last=True, num_workers=4, pin_memory=True)\n", "test_loader = data.DataLoader(test_set, batch_size=256, shuffle=False, drop_last=False, num_workers=4)"]}, {"cell_type": "markdown", "id": "3e1b26e0", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.02242, "end_time": "2021-09-16T12:40:41.378644", "exception": false, "start_time": "2021-09-16T12:40:41.356224", "status": "completed"}, "tags": []}, "source": ["### CNN Model\n", "\n", "First, we implement our CNN model.\n", "The MNIST images are of size 28x28, hence we only need a small model.\n", "As an example, we will apply several convolutions with stride 2 that downscale the images.\n", "If you are interested, you can also use a deeper model such as a small ResNet, but for simplicity,\n", "we will stick with the tiny network.\n", "\n", "It is a good practice to use a smooth activation function like Swish instead of ReLU in the energy model.\n", "This is because we will rely on the gradients we get back with respect to the input image, which should not be sparse."]}, {"cell_type": "code", "execution_count": 5, "id": "38169d71", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.429707Z", "iopub.status.busy": "2021-09-16T12:40:41.429207Z", "iopub.status.idle": "2021-09-16T12:40:41.431319Z", "shell.execute_reply": "2021-09-16T12:40:41.430920Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.030493, "end_time": "2021-09-16T12:40:41.431417", "exception": false, "start_time": "2021-09-16T12:40:41.400924", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class CNNModel(nn.Module):\n", " def __init__(self, hidden_features=32, out_dim=1, **kwargs):\n", " super().__init__()\n", " # We increase the hidden dimension over layers. Here pre-calculated for simplicity.\n", " c_hid1 = hidden_features // 2\n", " c_hid2 = hidden_features\n", " c_hid3 = hidden_features * 2\n", "\n", " # Series of convolutions and Swish activation functions\n", " self.cnn_layers = nn.Sequential(\n", " nn.Conv2d(1, c_hid1, kernel_size=5, stride=2, padding=4), # [16x16] - Larger padding to get 32x32 image\n", " nn.SiLU(),\n", " nn.Conv2d(c_hid1, c_hid2, kernel_size=3, stride=2, padding=1), # [8x8]\n", " nn.SiLU(),\n", " nn.Conv2d(c_hid2, c_hid3, kernel_size=3, stride=2, padding=1), # [4x4]\n", " nn.SiLU(),\n", " nn.Conv2d(c_hid3, c_hid3, kernel_size=3, stride=2, padding=1), # [2x2]\n", " nn.SiLU(),\n", " nn.Flatten(),\n", " nn.Linear(c_hid3 * 4, c_hid3),\n", " nn.SiLU(),\n", " nn.Linear(c_hid3, out_dim),\n", " )\n", "\n", " def forward(self, x):\n", " x = self.cnn_layers(x).squeeze(dim=-1)\n", " return x"]}, {"cell_type": "markdown", "id": "86a8d447", "metadata": {"papermill": {"duration": 0.022437, "end_time": "2021-09-16T12:40:41.476079", "exception": false, "start_time": "2021-09-16T12:40:41.453642", "status": "completed"}, "tags": []}, "source": ["In the rest of the notebook, the output of the model will actually not represent\n", "$E_{\\theta}(\\mathbf{x})$, but $-E_{\\theta}(\\mathbf{x})$.\n", "This is a standard implementation practice for energy-based models, as some people also write the energy probability\n", "density as $q_{\\theta}(\\mathbf{x}) = \\frac{\\exp\\left(f_{\\theta}(\\mathbf{x})\\right)}{Z_{\\theta}}$.\n", "In that case, the model would actually represent $f_{\\theta}(\\mathbf{x})$.\n", "In the training loss etc., we need to be careful to not switch up the signs."]}, {"cell_type": "markdown", "id": "5321df9e", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022306, "end_time": "2021-09-16T12:40:41.520797", "exception": false, "start_time": "2021-09-16T12:40:41.498491", "status": "completed"}, "tags": []}, "source": ["### Sampling buffer\n", "\n", "In the next part, we look at the training with sampled elements.\n", "To use the contrastive divergence objective, we need to generate samples during training.\n", "Previous work has shown that due to the high dimensionality of images, we need a lot of iterations\n", "inside the MCMC sampling to obtain reasonable samples.\n", "However, there is a training trick that significantly reduces the sampling cost: using a sampling buffer.\n", "The idea is that we store the samples of the last couple of batches in a buffer,\n", "and re-use those as the starting point of the MCMC algorithm for the next batches.\n", "This reduces the sampling cost because the model requires a significantly\n", "lower number of steps to converge to reasonable samples.\n", "However, to not solely rely on previous samples and allow novel samples as well,\n", "we re-initialize 5% of our samples from scratch (random noise between -1 and 1).\n", "\n", "Below, we implement the sampling buffer.\n", "The function `sample_new_exmps` returns a new batch of \"fake\" images.\n", "We refer to those as fake images because they have been generated, but are not actually part of the dataset.\n", "As mentioned before, we use initialize 5% randomly, and 95% are randomly picked from our buffer.\n", "On this initial batch, we perform MCMC for 60 iterations to improve the image quality\n", "and come closer to samples from $q_{\\theta}(\\mathbf{x})$.\n", "In the function `generate_samples`, we implemented the MCMC for images.\n", "Note that the hyperparameters of `step_size`, `steps`, the noise standard deviation\n", "$\\sigma$ are specifically set for MNIST, and need to be finetuned for a different dataset if you want to use such."]}, {"cell_type": "code", "execution_count": 6, "id": "84649cbd", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.577495Z", "iopub.status.busy": "2021-09-16T12:40:41.576997Z", "iopub.status.idle": "2021-09-16T12:40:41.579100Z", "shell.execute_reply": "2021-09-16T12:40:41.578638Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.035877, "end_time": "2021-09-16T12:40:41.579195", "exception": false, "start_time": "2021-09-16T12:40:41.543318", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class Sampler:\n", " def __init__(self, model, img_shape, sample_size, max_len=8192):\n", " \"\"\"\n", " Args:\n", " model: Neural network to use for modeling E_theta\n", " img_shape: Shape of the images to model\n", " sample_size: Batch size of the samples\n", " max_len: Maximum number of data points to keep in the buffer\n", " \"\"\"\n", " super().__init__()\n", " self.model = model\n", " self.img_shape = img_shape\n", " self.sample_size = sample_size\n", " self.max_len = max_len\n", " self.examples = [(torch.rand((1,) + img_shape) * 2 - 1) for _ in range(self.sample_size)]\n", "\n", " def sample_new_exmps(self, steps=60, step_size=10):\n", " \"\"\"Function for getting a new batch of \"fake\" images.\n", "\n", " Args:\n", " steps: Number of iterations in the MCMC algorithm\n", " step_size: Learning rate nu in the algorithm above\n", " \"\"\"\n", " # Choose 95% of the batch from the buffer, 5% generate from scratch\n", " n_new = np.random.binomial(self.sample_size, 0.05)\n", " rand_imgs = torch.rand((n_new,) + self.img_shape) * 2 - 1\n", " old_imgs = torch.cat(random.choices(self.examples, k=self.sample_size - n_new), dim=0)\n", " inp_imgs = torch.cat([rand_imgs, old_imgs], dim=0).detach().to(device)\n", "\n", " # Perform MCMC sampling\n", " inp_imgs = Sampler.generate_samples(self.model, inp_imgs, steps=steps, step_size=step_size)\n", "\n", " # Add new images to the buffer and remove old ones if needed\n", " self.examples = list(inp_imgs.to(torch.device(\"cpu\")).chunk(self.sample_size, dim=0)) + self.examples\n", " self.examples = self.examples[: self.max_len]\n", " return inp_imgs\n", "\n", " @staticmethod\n", " def generate_samples(model, inp_imgs, steps=60, step_size=10, return_img_per_step=False):\n", " \"\"\"Function for sampling images for a given model.\n", "\n", " Args:\n", " model: Neural network to use for modeling E_theta\n", " inp_imgs: Images to start from for sampling. If you want to generate new images, enter noise between -1 and 1.\n", " steps: Number of iterations in the MCMC algorithm.\n", " step_size: Learning rate nu in the algorithm above\n", " return_img_per_step: If True, we return the sample at every iteration of the MCMC\n", " \"\"\"\n", " # Before MCMC: set model parameters to \"required_grad=False\"\n", " # because we are only interested in the gradients of the input.\n", " is_training = model.training\n", " model.eval()\n", " for p in model.parameters():\n", " p.requires_grad = False\n", " inp_imgs.requires_grad = True\n", "\n", " # Enable gradient calculation if not already the case\n", " had_gradients_enabled = torch.is_grad_enabled()\n", " torch.set_grad_enabled(True)\n", "\n", " # We use a buffer tensor in which we generate noise each loop iteration.\n", " # More efficient than creating a new tensor every iteration.\n", " noise = torch.randn(inp_imgs.shape, device=inp_imgs.device)\n", "\n", " # List for storing generations at each step (for later analysis)\n", " imgs_per_step = []\n", "\n", " # Loop over K (steps)\n", " for _ in range(steps):\n", " # Part 1: Add noise to the input.\n", " noise.normal_(0, 0.005)\n", " inp_imgs.data.add_(noise.data)\n", " inp_imgs.data.clamp_(min=-1.0, max=1.0)\n", "\n", " # Part 2: calculate gradients for the current input.\n", " out_imgs = -model(inp_imgs)\n", " out_imgs.sum().backward()\n", " inp_imgs.grad.data.clamp_(-0.03, 0.03) # For stabilizing and preventing too high gradients\n", "\n", " # Apply gradients to our current samples\n", " inp_imgs.data.add_(-step_size * inp_imgs.grad.data)\n", " inp_imgs.grad.detach_()\n", " inp_imgs.grad.zero_()\n", " inp_imgs.data.clamp_(min=-1.0, max=1.0)\n", "\n", " if return_img_per_step:\n", " imgs_per_step.append(inp_imgs.clone().detach())\n", "\n", " # Reactivate gradients for parameters for training\n", " for p in model.parameters():\n", " p.requires_grad = True\n", " model.train(is_training)\n", "\n", " # Reset gradient calculation to setting before this function\n", " torch.set_grad_enabled(had_gradients_enabled)\n", "\n", " if return_img_per_step:\n", " return torch.stack(imgs_per_step, dim=0)\n", " else:\n", " return inp_imgs"]}, {"cell_type": "markdown", "id": "da0da692", "metadata": {"papermill": {"duration": 0.022214, "end_time": "2021-09-16T12:40:41.623643", "exception": false, "start_time": "2021-09-16T12:40:41.601429", "status": "completed"}, "tags": []}, "source": ["The idea of the buffer becomes a bit clearer in the following algorithm."]}, {"cell_type": "markdown", "id": "a39ea7ee", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022698, "end_time": "2021-09-16T12:40:41.668518", "exception": false, "start_time": "2021-09-16T12:40:41.645820", "status": "completed"}, "tags": []}, "source": ["### Training algorithm\n", "\n", "With the sampling buffer being ready, we can complete our training algorithm.\n", "Below is shown a summary of the full training algorithm of an energy model on image modeling:\n", "\n", "<center width=\"100%\" style=\"padding: 15px\"><img src=\"https://github.com/PyTorchLightning/lightning-tutorials/raw/main/course_UvA-DL/07-deep-energy-based-generative-models/training_algorithm.svg\" width=\"700px\"></center>\n", "\n", "The first few statements in each training iteration concern the sampling of the real and fake data,\n", "as we have seen above with the sample buffer.\n", "Next, we calculate the contrastive divergence objective using our energy model $E_{\\theta}$.\n", "However, one additional training trick we need is to add a regularization loss on the output of $E_{\\theta}$.\n", "As the output of the network is not constrained and adding a large bias or not to the output\n", "doesn't change the contrastive divergence loss, we need to ensure somehow else that the output values are in a reasonable range.\n", "Without the regularization loss, the output values will fluctuate in a very large range.\n", "With this, we ensure that the values for the real data are around 0, and the fake data likely slightly lower\n", "(for noise or outliers the score can be still significantly lower).\n", "As the regularization loss is less important than the Contrastive Divergence, we have a weight factor\n", "$\\alpha$ which is usually quite some smaller than 1.\n", "Finally, we perform an update step with an optimizer on the combined loss and add the new samples to the buffer.\n", "\n", "Below, we put this training dynamic into a PyTorch Lightning module:"]}, {"cell_type": "code", "execution_count": 7, "id": "5733f772", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.724998Z", "iopub.status.busy": "2021-09-16T12:40:41.717399Z", "iopub.status.idle": "2021-09-16T12:40:41.727028Z", "shell.execute_reply": "2021-09-16T12:40:41.726628Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.034742, "end_time": "2021-09-16T12:40:41.727126", "exception": false, "start_time": "2021-09-16T12:40:41.692384", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class DeepEnergyModel(pl.LightningModule):\n", " def __init__(self, img_shape, batch_size, alpha=0.1, lr=1e-4, beta1=0.0, **CNN_args):\n", " super().__init__()\n", " self.save_hyperparameters()\n", "\n", " self.cnn = CNNModel(**CNN_args)\n", " self.sampler = Sampler(self.cnn, img_shape=img_shape, sample_size=batch_size)\n", " self.example_input_array = torch.zeros(1, *img_shape)\n", "\n", " def forward(self, x):\n", " z = self.cnn(x)\n", " return z\n", "\n", " def configure_optimizers(self):\n", " # Energy models can have issues with momentum as the loss surfaces changes with its parameters.\n", " # Hence, we set it to 0 by default.\n", " optimizer = optim.Adam(self.parameters(), lr=self.hparams.lr, betas=(self.hparams.beta1, 0.999))\n", " scheduler = optim.lr_scheduler.StepLR(optimizer, 1, gamma=0.97) # Exponential decay over epochs\n", " return [optimizer], [scheduler]\n", "\n", " def training_step(self, batch, batch_idx):\n", " # We add minimal noise to the original images to prevent the model from focusing on purely \"clean\" inputs\n", " real_imgs, _ = batch\n", " small_noise = torch.randn_like(real_imgs) * 0.005\n", " real_imgs.add_(small_noise).clamp_(min=-1.0, max=1.0)\n", "\n", " # Obtain samples\n", " fake_imgs = self.sampler.sample_new_exmps(steps=60, step_size=10)\n", "\n", " # Predict energy score for all images\n", " inp_imgs = torch.cat([real_imgs, fake_imgs], dim=0)\n", " real_out, fake_out = self.cnn(inp_imgs).chunk(2, dim=0)\n", "\n", " # Calculate losses\n", " reg_loss = self.hparams.alpha * (real_out ** 2 + fake_out ** 2).mean()\n", " cdiv_loss = fake_out.mean() - real_out.mean()\n", " loss = reg_loss + cdiv_loss\n", "\n", " # Logging\n", " self.log(\"loss\", loss)\n", " self.log(\"loss_regularization\", reg_loss)\n", " self.log(\"loss_contrastive_divergence\", cdiv_loss)\n", " self.log(\"metrics_avg_real\", real_out.mean())\n", " self.log(\"metrics_avg_fake\", fake_out.mean())\n", " return loss\n", "\n", " def validation_step(self, batch, batch_idx):\n", " # For validating, we calculate the contrastive divergence between purely random images and unseen examples\n", " # Note that the validation/test step of energy-based models depends on what we are interested in the model\n", " real_imgs, _ = batch\n", " fake_imgs = torch.rand_like(real_imgs) * 2 - 1\n", "\n", " inp_imgs = torch.cat([real_imgs, fake_imgs], dim=0)\n", " real_out, fake_out = self.cnn(inp_imgs).chunk(2, dim=0)\n", "\n", " cdiv = fake_out.mean() - real_out.mean()\n", " self.log(\"val_contrastive_divergence\", cdiv)\n", " self.log(\"val_fake_out\", fake_out.mean())\n", " self.log(\"val_real_out\", real_out.mean())"]}, {"cell_type": "markdown", "id": "1ae0ae51", "metadata": {"papermill": {"duration": 0.022675, "end_time": "2021-09-16T12:40:41.772185", "exception": false, "start_time": "2021-09-16T12:40:41.749510", "status": "completed"}, "tags": []}, "source": ["We do not implement a test step because energy-based, generative models are usually not evaluated on a test set.\n", "The validation step however is used to get an idea of the difference between ennergy/likelihood\n", "of random images to unseen examples of the dataset."]}, {"cell_type": "markdown", "id": "6ae9a058", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022224, "end_time": "2021-09-16T12:40:41.816602", "exception": false, "start_time": "2021-09-16T12:40:41.794378", "status": "completed"}, "tags": []}, "source": ["### Callbacks\n", "\n", "To track the performance of our model during training, we will make extensive use of PyTorch Lightning's callback framework.\n", "Remember that callbacks can be used for running small functions at any point of the training,\n", "for instance after finishing an epoch.\n", "Here, we will use three different callbacks we define ourselves.\n", "\n", "The first callback, called `GenerateCallback`, is used for adding image generations to the model during training.\n", "After every $N$ epochs (usually $N=5$ to reduce output to TensorBoard), we take a small batch\n", "of random images and perform many MCMC iterations until the model's generation converges.\n", "Compared to the training that used 60 iterations, we use 256 here because\n", "(1) we only have to do it once compared to the training that has to do it every iteration, and\n", "(2) we do not start from a buffer here, but from scratch.\n", "It is implemented as follows:"]}, {"cell_type": "code", "execution_count": 8, "id": "553fb562", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.868808Z", "iopub.status.busy": "2021-09-16T12:40:41.868332Z", "iopub.status.idle": "2021-09-16T12:40:41.870405Z", "shell.execute_reply": "2021-09-16T12:40:41.870008Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.031581, "end_time": "2021-09-16T12:40:41.870500", "exception": false, "start_time": "2021-09-16T12:40:41.838919", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class GenerateCallback(pl.Callback):\n", " def __init__(self, batch_size=8, vis_steps=8, num_steps=256, every_n_epochs=5):\n", " super().__init__()\n", " self.batch_size = batch_size # Number of images to generate\n", " self.vis_steps = vis_steps # Number of steps within generation to visualize\n", " self.num_steps = num_steps # Number of steps to take during generation\n", " # Only save those images every N epochs (otherwise tensorboard gets quite large)\n", " self.every_n_epochs = every_n_epochs\n", "\n", " def on_epoch_end(self, trainer, pl_module):\n", " # Skip for all other epochs\n", " if trainer.current_epoch % self.every_n_epochs == 0:\n", " # Generate images\n", " imgs_per_step = self.generate_imgs(pl_module)\n", " # Plot and add to tensorboard\n", " for i in range(imgs_per_step.shape[1]):\n", " step_size = self.num_steps // self.vis_steps\n", " imgs_to_plot = imgs_per_step[step_size - 1 :: step_size, i]\n", " grid = torchvision.utils.make_grid(\n", " imgs_to_plot, nrow=imgs_to_plot.shape[0], normalize=True, range=(-1, 1)\n", " )\n", " trainer.logger.experiment.add_image(\"generation_%i\" % i, grid, global_step=trainer.current_epoch)\n", "\n", " def generate_imgs(self, pl_module):\n", " pl_module.eval()\n", " start_imgs = torch.rand((self.batch_size,) + pl_module.hparams[\"img_shape\"]).to(pl_module.device)\n", " start_imgs = start_imgs * 2 - 1\n", " imgs_per_step = Sampler.generate_samples(\n", " pl_module.cnn, start_imgs, steps=self.num_steps, step_size=10, return_img_per_step=True\n", " )\n", " pl_module.train()\n", " return imgs_per_step"]}, {"cell_type": "markdown", "id": "10fb6c28", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022491, "end_time": "2021-09-16T12:40:41.915420", "exception": false, "start_time": "2021-09-16T12:40:41.892929", "status": "completed"}, "tags": []}, "source": ["The second callback is called `SamplerCallback`, and simply adds a randomly picked subset of images\n", "in the sampling buffer to the TensorBoard.\n", "This helps to understand what images are currently shown to the model as \"fake\"."]}, {"cell_type": "code", "execution_count": 9, "id": "d973c3d0", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:41.965194Z", "iopub.status.busy": "2021-09-16T12:40:41.964725Z", "iopub.status.idle": "2021-09-16T12:40:41.966940Z", "shell.execute_reply": "2021-09-16T12:40:41.966479Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.029353, "end_time": "2021-09-16T12:40:41.967038", "exception": false, "start_time": "2021-09-16T12:40:41.937685", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class SamplerCallback(pl.Callback):\n", " def __init__(self, num_imgs=32, every_n_epochs=5):\n", " super().__init__()\n", " self.num_imgs = num_imgs # Number of images to plot\n", " # Only save those images every N epochs (otherwise tensorboard gets quite large)\n", " self.every_n_epochs = every_n_epochs\n", "\n", " def on_epoch_end(self, trainer, pl_module):\n", " if trainer.current_epoch % self.every_n_epochs == 0:\n", " exmp_imgs = torch.cat(random.choices(pl_module.sampler.examples, k=self.num_imgs), dim=0)\n", " grid = torchvision.utils.make_grid(exmp_imgs, nrow=4, normalize=True, range=(-1, 1))\n", " trainer.logger.experiment.add_image(\"sampler\", grid, global_step=trainer.current_epoch)"]}, {"cell_type": "markdown", "id": "adaa80d7", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022387, "end_time": "2021-09-16T12:40:42.011824", "exception": false, "start_time": "2021-09-16T12:40:41.989437", "status": "completed"}, "tags": []}, "source": ["Finally, our last callback is `OutlierCallback`.\n", "This callback evaluates the model by recording the (negative) energy assigned to random noise.\n", "While our training loss is almost constant across iterations,\n", "this score is likely showing the progress of the model to detect \"outliers\"."]}, {"cell_type": "code", "execution_count": 10, "id": "9ac8745d", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:42.064684Z", "iopub.status.busy": "2021-09-16T12:40:42.064208Z", "iopub.status.idle": "2021-09-16T12:40:42.066806Z", "shell.execute_reply": "2021-09-16T12:40:42.066321Z"}, "lines_to_next_cell": 2, "papermill": {"duration": 0.03245, "end_time": "2021-09-16T12:40:42.066912", "exception": false, "start_time": "2021-09-16T12:40:42.034462", "status": "completed"}, "tags": []}, "outputs": [], "source": ["class OutlierCallback(pl.Callback):\n", " def __init__(self, batch_size=1024):\n", " super().__init__()\n", " self.batch_size = batch_size\n", "\n", " def on_epoch_end(self, trainer, pl_module):\n", " with torch.no_grad():\n", " pl_module.eval()\n", " rand_imgs = torch.rand((self.batch_size,) + pl_module.hparams[\"img_shape\"]).to(pl_module.device)\n", " rand_imgs = rand_imgs * 2 - 1.0\n", " rand_out = pl_module.cnn(rand_imgs).mean()\n", " pl_module.train()\n", "\n", " trainer.logger.experiment.add_scalar(\"rand_out\", rand_out, global_step=trainer.current_epoch)"]}, {"cell_type": "markdown", "id": "70834e47", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.022843, "end_time": "2021-09-16T12:40:42.112671", "exception": false, "start_time": "2021-09-16T12:40:42.089828", "status": "completed"}, "tags": []}, "source": ["### Running the model\n", "\n", "Finally, we can add everything together to create our final training function.\n", "The function is very similar to any other PyTorch Lightning training function we have seen so far.\n", "However, there is the small difference of that we do not test the model on a test set\n", "because we will analyse the model afterward by checking its prediction and ability to perform outlier detection."]}, {"cell_type": "code", "execution_count": 11, "id": "5561a42f", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:42.164214Z", "iopub.status.busy": "2021-09-16T12:40:42.163735Z", "iopub.status.idle": "2021-09-16T12:40:42.165765Z", "shell.execute_reply": "2021-09-16T12:40:42.165284Z"}, "papermill": {"duration": 0.030454, "end_time": "2021-09-16T12:40:42.165867", "exception": false, "start_time": "2021-09-16T12:40:42.135413", "status": "completed"}, "tags": []}, "outputs": [], "source": ["def train_model(**kwargs):\n", " # Create a PyTorch Lightning trainer with the generation callback\n", " trainer = pl.Trainer(\n", " default_root_dir=os.path.join(CHECKPOINT_PATH, \"MNIST\"),\n", " gpus=1 if str(device).startswith(\"cuda\") else 0,\n", " max_epochs=60,\n", " gradient_clip_val=0.1,\n", " callbacks=[\n", " ModelCheckpoint(save_weights_only=True, mode=\"min\", monitor=\"val_contrastive_divergence\"),\n", " GenerateCallback(every_n_epochs=5),\n", " SamplerCallback(every_n_epochs=5),\n", " OutlierCallback(),\n", " LearningRateMonitor(\"epoch\"),\n", " ],\n", " progress_bar_refresh_rate=1,\n", " )\n", " # Check whether pretrained model exists. If yes, load it and skip training\n", " pretrained_filename = os.path.join(CHECKPOINT_PATH, \"MNIST.ckpt\")\n", " if os.path.isfile(pretrained_filename):\n", " print(\"Found pretrained model, loading...\")\n", " model = DeepEnergyModel.load_from_checkpoint(pretrained_filename)\n", " else:\n", " pl.seed_everything(42)\n", " model = DeepEnergyModel(**kwargs)\n", " trainer.fit(model, train_loader, test_loader)\n", " model = DeepEnergyModel.load_from_checkpoint(trainer.checkpoint_callback.best_model_path)\n", " # No testing as we are more interested in other properties\n", " return model"]}, {"cell_type": "code", "execution_count": 12, "id": "0d734155", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:42.214793Z", "iopub.status.busy": "2021-09-16T12:40:42.214331Z", "iopub.status.idle": "2021-09-16T12:40:42.228657Z", "shell.execute_reply": "2021-09-16T12:40:42.229038Z"}, "papermill": {"duration": 0.040314, "end_time": "2021-09-16T12:40:42.229150", "exception": false, "start_time": "2021-09-16T12:40:42.188836", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["GPU available: True, used: True\n"]}, {"name": "stderr", "output_type": "stream", "text": ["TPU available: False, using: 0 TPU cores\n"]}, {"name": "stderr", "output_type": "stream", "text": ["IPU available: False, using: 0 IPUs\n"]}, {"name": "stdout", "output_type": "stream", "text": ["Found pretrained model, loading...\n"]}], "source": ["model = train_model(img_shape=(1, 28, 28), batch_size=train_loader.batch_size, lr=1e-4, beta1=0.0)"]}, {"cell_type": "markdown", "id": "3de610c0", "metadata": {"papermill": {"duration": 0.023634, "end_time": "2021-09-16T12:40:42.276465", "exception": false, "start_time": "2021-09-16T12:40:42.252831", "status": "completed"}, "tags": []}, "source": ["## Analysis\n", "\n", "In the last part of the notebook, we will try to take the trained energy-based generative model,\n", "and analyse its properties."]}, {"cell_type": "markdown", "id": "879c2039", "metadata": {"papermill": {"duration": 0.023472, "end_time": "2021-09-16T12:40:42.323822", "exception": false, "start_time": "2021-09-16T12:40:42.300350", "status": "completed"}, "tags": []}, "source": ["### TensorBoard\n", "\n", "The first thing we can look at is the TensorBoard generate during training.\n", "This can help us to understand the training dynamic even better, and shows potential issues.\n", "Let's load the TensorBoard below:"]}, {"cell_type": "code", "execution_count": 13, "id": "c4ffadfc", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:42.374084Z", "iopub.status.busy": "2021-09-16T12:40:42.373589Z", "iopub.status.idle": "2021-09-16T12:40:42.375710Z", "shell.execute_reply": "2021-09-16T12:40:42.375247Z"}, "papermill": {"duration": 0.028238, "end_time": "2021-09-16T12:40:42.375807", "exception": false, "start_time": "2021-09-16T12:40:42.347569", "status": "completed"}, "tags": []}, "outputs": [], "source": ["# Uncomment the following two lines to open a tensorboard in the notebook.\n", "# Adjust the path to your CHECKPOINT_PATH if needed.\n", "# %load_ext tensorboard\n", "# %tensorboard --logdir ../saved_models/tutorial8/tensorboards/"]}, {"cell_type": "markdown", "id": "c7b8f333", "metadata": {"papermill": {"duration": 0.023692, "end_time": "2021-09-16T12:40:42.423585", "exception": false, "start_time": "2021-09-16T12:40:42.399893", "status": "completed"}, "tags": []}, "source": ["<center width=\"100%\"><img src=\"https://github.com/PyTorchLightning/lightning-tutorials/raw/main/course_UvA-DL/07-deep-energy-based-generative-models/tensorboard_screenshot.png\" width=\"1000px\"></center>"]}, {"cell_type": "markdown", "id": "e608ca53", "metadata": {"papermill": {"duration": 0.023833, "end_time": "2021-09-16T12:40:42.471015", "exception": false, "start_time": "2021-09-16T12:40:42.447182", "status": "completed"}, "tags": []}, "source": ["We see that the contrastive divergence as well as the regularization converge quickly to 0.\n", "However, the training continues although the loss is always close to zero.\n", "This is because our \"training\" data changes with the model by sampling.\n", "The progress of training can be best measured by looking at the samples across iterations,\n", "and the score for random images that decreases constantly over time."]}, {"cell_type": "markdown", "id": "a1184e57", "metadata": {"papermill": {"duration": 0.023719, "end_time": "2021-09-16T12:40:42.518253", "exception": false, "start_time": "2021-09-16T12:40:42.494534", "status": "completed"}, "tags": []}, "source": ["### Image Generation\n", "\n", "Another way of evaluating generative models is by sampling a few generated images.\n", "Generative models need to be good at generating realistic images as this truely shows that they have modeled the true data distribution.\n", "Thus, let's sample a few images of the model below:"]}, {"cell_type": "code", "execution_count": 14, "id": "f84da507", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:42.570336Z", "iopub.status.busy": "2021-09-16T12:40:42.569866Z", "iopub.status.idle": "2021-09-16T12:40:45.522168Z", "shell.execute_reply": "2021-09-16T12:40:45.521632Z"}, "papermill": {"duration": 2.980431, "end_time": "2021-09-16T12:40:45.522288", "exception": false, "start_time": "2021-09-16T12:40:42.541857", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["Global seed set to 43\n"]}], "source": ["model.to(device)\n", "pl.seed_everything(43)\n", "callback = GenerateCallback(batch_size=4, vis_steps=8, num_steps=256)\n", "imgs_per_step = callback.generate_imgs(model)\n", "imgs_per_step = imgs_per_step.cpu()"]}, {"cell_type": "markdown", "id": "96a6dec4", "metadata": {"papermill": {"duration": 0.260591, "end_time": "2021-09-16T12:40:45.862389", "exception": false, "start_time": "2021-09-16T12:40:45.601798", "status": "completed"}, "tags": []}, "source": ["The characteristic of sampling with energy-based models is that they require the iterative MCMC algorithm.\n", "To gain an insight in how the images change over iterations, we plot a few intermediate samples in the MCMC as well:"]}, {"cell_type": "code", "execution_count": 15, "id": "8a53c31a", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:46.095876Z", "iopub.status.busy": "2021-09-16T12:40:46.095395Z", "iopub.status.idle": "2021-09-16T12:40:46.738218Z", "shell.execute_reply": "2021-09-16T12:40:46.738604Z"}, "papermill": {"duration": 0.675706, "end_time": "2021-09-16T12:40:46.738750", "exception": false, "start_time": "2021-09-16T12:40:46.063044", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"97.273897pt\" version=\"1.1\" viewBox=\"0 0 464.3 97.273897\" width=\"464.3pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:46.157923</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 97.273897 \n", "L 464.3 97.273897 \n", "L 464.3 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "L 457.1 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#pf6dafbba2b)\">\n", " <image height=\"53\" id=\"image4d73a74f94\" transform=\"scale(1 -1)translate(0 -53)\" width=\"447\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.717647\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"m78502d90d7\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.138235\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- 1 -->\n", " <g transform=\"translate(32.956985 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 794 531 \n", "L 1825 531 \n", "L 1825 4091 \n", "L 703 3866 \n", "L 703 4441 \n", "L 1819 4666 \n", "L 2450 4666 \n", "L 2450 531 \n", "L 3481 531 \n", "L 3481 0 \n", "L 794 0 \n", "L 794 531 \n", "z\n", "\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"85.373529\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- 32 -->\n", " <g transform=\"translate(79.011029 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2597 2516 \n", "Q 3050 2419 3304 2112 \n", "Q 3559 1806 3559 1356 \n", "Q 3559 666 3084 287 \n", "Q 2609 -91 1734 -91 \n", "Q 1441 -91 1130 -33 \n", "Q 819 25 488 141 \n", "L 488 750 \n", "Q 750 597 1062 519 \n", "Q 1375 441 1716 441 \n", "Q 2309 441 2620 675 \n", "Q 2931 909 2931 1356 \n", "Q 2931 1769 2642 2001 \n", "Q 2353 2234 1838 2234 \n", "L 1294 2234 \n", "L 1294 2753 \n", "L 1863 2753 \n", "Q 2328 2753 2575 2939 \n", "Q 2822 3125 2822 3475 \n", "Q 2822 3834 2567 4026 \n", "Q 2313 4219 1838 4219 \n", "Q 1578 4219 1281 4162 \n", "Q 984 4106 628 3988 \n", "L 628 4550 \n", "Q 988 4650 1302 4700 \n", "Q 1616 4750 1894 4750 \n", "Q 2613 4750 3031 4423 \n", "Q 3450 4097 3450 3541 \n", "Q 3450 3153 3228 2886 \n", "Q 3006 2619 2597 2516 \n", "z\n", "\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1228 531 \n", "L 3431 531 \n", "L 3431 0 \n", "L 469 0 \n", "L 469 531 \n", "Q 828 903 1448 1529 \n", "Q 2069 2156 2228 2338 \n", "Q 2531 2678 2651 2914 \n", "Q 2772 3150 2772 3378 \n", "Q 2772 3750 2511 3984 \n", "Q 2250 4219 1831 4219 \n", "Q 1534 4219 1204 4116 \n", "Q 875 4013 500 3803 \n", "L 500 4441 \n", "Q 881 4594 1212 4672 \n", "Q 1544 4750 1819 4750 \n", "Q 2544 4750 2975 4387 \n", "Q 3406 4025 3406 3419 \n", "Q 3406 3131 3298 2873 \n", "Q 3191 2616 2906 2266 \n", "Q 2828 2175 2409 1742 \n", "Q 1991 1309 1228 531 \n", "z\n", "\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-33\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_3\">\n", " <g id=\"line2d_3\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"134.608824\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_3\">\n", " <!-- 64 -->\n", " <g transform=\"translate(128.246324 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2113 2584 \n", "Q 1688 2584 1439 2293 \n", "Q 1191 2003 1191 1497 \n", "Q 1191 994 1439 701 \n", "Q 1688 409 2113 409 \n", "Q 2538 409 2786 701 \n", "Q 3034 994 3034 1497 \n", "Q 3034 2003 2786 2293 \n", "Q 2538 2584 2113 2584 \n", "z\n", "M 3366 4563 \n", "L 3366 3988 \n", "Q 3128 4100 2886 4159 \n", "Q 2644 4219 2406 4219 \n", "Q 1781 4219 1451 3797 \n", "Q 1122 3375 1075 2522 \n", "Q 1259 2794 1537 2939 \n", "Q 1816 3084 2150 3084 \n", "Q 2853 3084 3261 2657 \n", "Q 3669 2231 3669 1497 \n", "Q 3669 778 3244 343 \n", "Q 2819 -91 2113 -91 \n", "Q 1303 -91 875 529 \n", "Q 447 1150 447 2328 \n", "Q 447 3434 972 4092 \n", "Q 1497 4750 2381 4750 \n", "Q 2619 4750 2861 4703 \n", "Q 3103 4656 3366 4563 \n", "z\n", "\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2419 4116 \n", "L 825 1625 \n", "L 2419 1625 \n", "L 2419 4116 \n", "z\n", "M 2253 4666 \n", "L 3047 4666 \n", "L 3047 1625 \n", "L 3713 1625 \n", "L 3713 1100 \n", "L 3047 1100 \n", "L 3047 0 \n", "L 2419 0 \n", "L 2419 1100 \n", "L 313 1100 \n", "L 313 1709 \n", "L 2253 4666 \n", "z\n", "\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_4\">\n", " <g id=\"line2d_4\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"183.844118\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_4\">\n", " <!-- 96 -->\n", " <g transform=\"translate(177.481618 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 703 97 \n", "L 703 672 \n", "Q 941 559 1184 500 \n", "Q 1428 441 1663 441 \n", "Q 2288 441 2617 861 \n", "Q 2947 1281 2994 2138 \n", "Q 2813 1869 2534 1725 \n", "Q 2256 1581 1919 1581 \n", "Q 1219 1581 811 2004 \n", "Q 403 2428 403 3163 \n", "Q 403 3881 828 4315 \n", "Q 1253 4750 1959 4750 \n", "Q 2769 4750 3195 4129 \n", "Q 3622 3509 3622 2328 \n", "Q 3622 1225 3098 567 \n", "Q 2575 -91 1691 -91 \n", "Q 1453 -91 1209 -44 \n", "Q 966 3 703 97 \n", "z\n", "M 1959 2075 \n", "Q 2384 2075 2632 2365 \n", "Q 2881 2656 2881 3163 \n", "Q 2881 3666 2632 3958 \n", "Q 2384 4250 1959 4250 \n", "Q 1534 4250 1286 3958 \n", "Q 1038 3666 1038 3163 \n", "Q 1038 2656 1286 2365 \n", "Q 1534 2075 1959 2075 \n", "z\n", "\" id=\"DejaVuSans-39\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_5\">\n", " <g id=\"line2d_5\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"233.079412\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_5\">\n", " <!-- 128 -->\n", " <g transform=\"translate(223.535662 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 2216 \n", "Q 1584 2216 1326 1975 \n", "Q 1069 1734 1069 1313 \n", "Q 1069 891 1326 650 \n", "Q 1584 409 2034 409 \n", "Q 2484 409 2743 651 \n", "Q 3003 894 3003 1313 \n", "Q 3003 1734 2745 1975 \n", "Q 2488 2216 2034 2216 \n", "z\n", "M 1403 2484 \n", "Q 997 2584 770 2862 \n", "Q 544 3141 544 3541 \n", "Q 544 4100 942 4425 \n", "Q 1341 4750 2034 4750 \n", "Q 2731 4750 3128 4425 \n", "Q 3525 4100 3525 3541 \n", "Q 3525 3141 3298 2862 \n", "Q 3072 2584 2669 2484 \n", "Q 3125 2378 3379 2068 \n", "Q 3634 1759 3634 1313 \n", "Q 3634 634 3220 271 \n", "Q 2806 -91 2034 -91 \n", "Q 1263 -91 848 271 \n", "Q 434 634 434 1313 \n", "Q 434 1759 690 2068 \n", "Q 947 2378 1403 2484 \n", "z\n", "M 1172 3481 \n", "Q 1172 3119 1398 2916 \n", "Q 1625 2713 2034 2713 \n", "Q 2441 2713 2670 2916 \n", "Q 2900 3119 2900 3481 \n", "Q 2900 3844 2670 4047 \n", "Q 2441 4250 2034 4250 \n", "Q 1625 4250 1398 4047 \n", "Q 1172 3844 1172 3481 \n", "z\n", "\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-38\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_6\">\n", " <g id=\"line2d_6\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.314706\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_6\">\n", " <!-- 160 -->\n", " <g transform=\"translate(272.770956 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 4250 \n", "Q 1547 4250 1301 3770 \n", "Q 1056 3291 1056 2328 \n", "Q 1056 1369 1301 889 \n", "Q 1547 409 2034 409 \n", "Q 2525 409 2770 889 \n", "Q 3016 1369 3016 2328 \n", "Q 3016 3291 2770 3770 \n", "Q 2525 4250 2034 4250 \n", "z\n", "M 2034 4750 \n", "Q 2819 4750 3233 4129 \n", "Q 3647 3509 3647 2328 \n", "Q 3647 1150 3233 529 \n", "Q 2819 -91 2034 -91 \n", "Q 1250 -91 836 529 \n", "Q 422 1150 422 2328 \n", "Q 422 3509 836 4129 \n", "Q 1250 4750 2034 4750 \n", "z\n", "\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-30\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_7\">\n", " <g id=\"line2d_7\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"331.55\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_7\">\n", " <!-- 192 -->\n", " <g transform=\"translate(322.00625 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_8\">\n", " <g id=\"line2d_8\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"380.785294\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_8\">\n", " <!-- 224 -->\n", " <g transform=\"translate(371.241544 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_9\">\n", " <g id=\"line2d_9\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"430.020588\" xlink:href=\"#m78502d90d7\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_9\">\n", " <!-- 256 -->\n", " <g transform=\"translate(420.476838 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 691 4666 \n", "L 3169 4666 \n", "L 3169 4134 \n", "L 1269 4134 \n", "L 1269 2991 \n", "Q 1406 3038 1543 3061 \n", "Q 1681 3084 1819 3084 \n", "Q 2600 3084 3056 2656 \n", "Q 3513 2228 3513 1497 \n", "Q 3513 744 3044 326 \n", "Q 2575 -91 1722 -91 \n", "Q 1428 -91 1123 -41 \n", "Q 819 9 494 109 \n", "L 494 744 \n", "Q 775 591 1075 516 \n", "Q 1375 441 1709 441 \n", "Q 2250 441 2565 725 \n", "Q 2881 1009 2881 1497 \n", "Q 2881 1984 2565 2268 \n", "Q 2250 2553 1709 2553 \n", "Q 1456 2553 1204 2497 \n", "Q 953 2441 691 2322 \n", "L 691 4666 \n", "z\n", "\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-35\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_10\">\n", " <!-- Generation iteration -->\n", " <g transform=\"translate(183.295312 87.99421)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 3809 666 \n", "L 3809 1919 \n", "L 2778 1919 \n", "L 2778 2438 \n", "L 4434 2438 \n", "L 4434 434 \n", "Q 4069 175 3628 42 \n", "Q 3188 -91 2688 -91 \n", "Q 1594 -91 976 548 \n", "Q 359 1188 359 2328 \n", "Q 359 3472 976 4111 \n", "Q 1594 4750 2688 4750 \n", "Q 3144 4750 3555 4637 \n", "Q 3966 4525 4313 4306 \n", "L 4313 3634 \n", "Q 3963 3931 3569 4081 \n", "Q 3175 4231 2741 4231 \n", "Q 1884 4231 1454 3753 \n", "Q 1025 3275 1025 2328 \n", "Q 1025 1384 1454 906 \n", "Q 1884 428 2741 428 \n", "Q 3075 428 3337 486 \n", "Q 3600 544 3809 666 \n", "z\n", "\" id=\"DejaVuSans-47\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1172 4494 \n", "L 1172 3500 \n", "L 2356 3500 \n", "L 2356 3053 \n", "L 1172 3053 \n", "L 1172 1153 \n", "Q 1172 725 1289 603 \n", "Q 1406 481 1766 481 \n", "L 2356 481 \n", "L 2356 0 \n", "L 1766 0 \n", "Q 1100 0 847 248 \n", "Q 594 497 594 1153 \n", "L 594 3053 \n", "L 172 3053 \n", "L 172 3500 \n", "L 594 3500 \n", "L 594 4494 \n", "L 1172 4494 \n", "z\n", "\" id=\"DejaVuSans-74\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-47\"/>\n", " <use x=\"77.490234\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"139.013672\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"202.392578\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"263.916016\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"305.029297\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"366.308594\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"405.517578\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"433.300781\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"494.482422\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"557.861328\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"589.648438\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"617.431641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"656.640625\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"718.164062\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"759.277344\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"820.556641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"859.765625\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"887.548828\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"948.730469\" xlink:href=\"#DejaVuSans-6e\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 59.717647 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 457.1 59.717647 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"pf6dafbba2b\">\n", " <rect height=\"52.517647\" width=\"446.4\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 576x576 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"97.273897pt\" version=\"1.1\" viewBox=\"0 0 464.3 97.273897\" width=\"464.3pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:46.343108</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 97.273897 \n", "L 464.3 97.273897 \n", "L 464.3 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "L 457.1 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#p245c227725)\">\n", " <image height=\"53\" id=\"imagef810355ebb\" transform=\"scale(1 -1)translate(0 -53)\" width=\"447\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.717647\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"m088cb034ce\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.138235\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- 1 -->\n", " <g transform=\"translate(32.956985 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 794 531 \n", "L 1825 531 \n", "L 1825 4091 \n", "L 703 3866 \n", "L 703 4441 \n", "L 1819 4666 \n", "L 2450 4666 \n", "L 2450 531 \n", "L 3481 531 \n", "L 3481 0 \n", "L 794 0 \n", "L 794 531 \n", "z\n", "\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"85.373529\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- 32 -->\n", " <g transform=\"translate(79.011029 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2597 2516 \n", "Q 3050 2419 3304 2112 \n", "Q 3559 1806 3559 1356 \n", "Q 3559 666 3084 287 \n", "Q 2609 -91 1734 -91 \n", "Q 1441 -91 1130 -33 \n", "Q 819 25 488 141 \n", "L 488 750 \n", "Q 750 597 1062 519 \n", "Q 1375 441 1716 441 \n", "Q 2309 441 2620 675 \n", "Q 2931 909 2931 1356 \n", "Q 2931 1769 2642 2001 \n", "Q 2353 2234 1838 2234 \n", "L 1294 2234 \n", "L 1294 2753 \n", "L 1863 2753 \n", "Q 2328 2753 2575 2939 \n", "Q 2822 3125 2822 3475 \n", "Q 2822 3834 2567 4026 \n", "Q 2313 4219 1838 4219 \n", "Q 1578 4219 1281 4162 \n", "Q 984 4106 628 3988 \n", "L 628 4550 \n", "Q 988 4650 1302 4700 \n", "Q 1616 4750 1894 4750 \n", "Q 2613 4750 3031 4423 \n", "Q 3450 4097 3450 3541 \n", "Q 3450 3153 3228 2886 \n", "Q 3006 2619 2597 2516 \n", "z\n", "\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1228 531 \n", "L 3431 531 \n", "L 3431 0 \n", "L 469 0 \n", "L 469 531 \n", "Q 828 903 1448 1529 \n", "Q 2069 2156 2228 2338 \n", "Q 2531 2678 2651 2914 \n", "Q 2772 3150 2772 3378 \n", "Q 2772 3750 2511 3984 \n", "Q 2250 4219 1831 4219 \n", "Q 1534 4219 1204 4116 \n", "Q 875 4013 500 3803 \n", "L 500 4441 \n", "Q 881 4594 1212 4672 \n", "Q 1544 4750 1819 4750 \n", "Q 2544 4750 2975 4387 \n", "Q 3406 4025 3406 3419 \n", "Q 3406 3131 3298 2873 \n", "Q 3191 2616 2906 2266 \n", "Q 2828 2175 2409 1742 \n", "Q 1991 1309 1228 531 \n", "z\n", "\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-33\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_3\">\n", " <g id=\"line2d_3\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"134.608824\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_3\">\n", " <!-- 64 -->\n", " <g transform=\"translate(128.246324 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2113 2584 \n", "Q 1688 2584 1439 2293 \n", "Q 1191 2003 1191 1497 \n", "Q 1191 994 1439 701 \n", "Q 1688 409 2113 409 \n", "Q 2538 409 2786 701 \n", "Q 3034 994 3034 1497 \n", "Q 3034 2003 2786 2293 \n", "Q 2538 2584 2113 2584 \n", "z\n", "M 3366 4563 \n", "L 3366 3988 \n", "Q 3128 4100 2886 4159 \n", "Q 2644 4219 2406 4219 \n", "Q 1781 4219 1451 3797 \n", "Q 1122 3375 1075 2522 \n", "Q 1259 2794 1537 2939 \n", "Q 1816 3084 2150 3084 \n", "Q 2853 3084 3261 2657 \n", "Q 3669 2231 3669 1497 \n", "Q 3669 778 3244 343 \n", "Q 2819 -91 2113 -91 \n", "Q 1303 -91 875 529 \n", "Q 447 1150 447 2328 \n", "Q 447 3434 972 4092 \n", "Q 1497 4750 2381 4750 \n", "Q 2619 4750 2861 4703 \n", "Q 3103 4656 3366 4563 \n", "z\n", "\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2419 4116 \n", "L 825 1625 \n", "L 2419 1625 \n", "L 2419 4116 \n", "z\n", "M 2253 4666 \n", "L 3047 4666 \n", "L 3047 1625 \n", "L 3713 1625 \n", "L 3713 1100 \n", "L 3047 1100 \n", "L 3047 0 \n", "L 2419 0 \n", "L 2419 1100 \n", "L 313 1100 \n", "L 313 1709 \n", "L 2253 4666 \n", "z\n", "\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_4\">\n", " <g id=\"line2d_4\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"183.844118\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_4\">\n", " <!-- 96 -->\n", " <g transform=\"translate(177.481618 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 703 97 \n", "L 703 672 \n", "Q 941 559 1184 500 \n", "Q 1428 441 1663 441 \n", "Q 2288 441 2617 861 \n", "Q 2947 1281 2994 2138 \n", "Q 2813 1869 2534 1725 \n", "Q 2256 1581 1919 1581 \n", "Q 1219 1581 811 2004 \n", "Q 403 2428 403 3163 \n", "Q 403 3881 828 4315 \n", "Q 1253 4750 1959 4750 \n", "Q 2769 4750 3195 4129 \n", "Q 3622 3509 3622 2328 \n", "Q 3622 1225 3098 567 \n", "Q 2575 -91 1691 -91 \n", "Q 1453 -91 1209 -44 \n", "Q 966 3 703 97 \n", "z\n", "M 1959 2075 \n", "Q 2384 2075 2632 2365 \n", "Q 2881 2656 2881 3163 \n", "Q 2881 3666 2632 3958 \n", "Q 2384 4250 1959 4250 \n", "Q 1534 4250 1286 3958 \n", "Q 1038 3666 1038 3163 \n", "Q 1038 2656 1286 2365 \n", "Q 1534 2075 1959 2075 \n", "z\n", "\" id=\"DejaVuSans-39\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_5\">\n", " <g id=\"line2d_5\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"233.079412\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_5\">\n", " <!-- 128 -->\n", " <g transform=\"translate(223.535662 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 2216 \n", "Q 1584 2216 1326 1975 \n", "Q 1069 1734 1069 1313 \n", "Q 1069 891 1326 650 \n", "Q 1584 409 2034 409 \n", "Q 2484 409 2743 651 \n", "Q 3003 894 3003 1313 \n", "Q 3003 1734 2745 1975 \n", "Q 2488 2216 2034 2216 \n", "z\n", "M 1403 2484 \n", "Q 997 2584 770 2862 \n", "Q 544 3141 544 3541 \n", "Q 544 4100 942 4425 \n", "Q 1341 4750 2034 4750 \n", "Q 2731 4750 3128 4425 \n", "Q 3525 4100 3525 3541 \n", "Q 3525 3141 3298 2862 \n", "Q 3072 2584 2669 2484 \n", "Q 3125 2378 3379 2068 \n", "Q 3634 1759 3634 1313 \n", "Q 3634 634 3220 271 \n", "Q 2806 -91 2034 -91 \n", "Q 1263 -91 848 271 \n", "Q 434 634 434 1313 \n", "Q 434 1759 690 2068 \n", "Q 947 2378 1403 2484 \n", "z\n", "M 1172 3481 \n", "Q 1172 3119 1398 2916 \n", "Q 1625 2713 2034 2713 \n", "Q 2441 2713 2670 2916 \n", "Q 2900 3119 2900 3481 \n", "Q 2900 3844 2670 4047 \n", "Q 2441 4250 2034 4250 \n", "Q 1625 4250 1398 4047 \n", "Q 1172 3844 1172 3481 \n", "z\n", "\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-38\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_6\">\n", " <g id=\"line2d_6\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.314706\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_6\">\n", " <!-- 160 -->\n", " <g transform=\"translate(272.770956 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 4250 \n", "Q 1547 4250 1301 3770 \n", "Q 1056 3291 1056 2328 \n", "Q 1056 1369 1301 889 \n", "Q 1547 409 2034 409 \n", "Q 2525 409 2770 889 \n", "Q 3016 1369 3016 2328 \n", "Q 3016 3291 2770 3770 \n", "Q 2525 4250 2034 4250 \n", "z\n", "M 2034 4750 \n", "Q 2819 4750 3233 4129 \n", "Q 3647 3509 3647 2328 \n", "Q 3647 1150 3233 529 \n", "Q 2819 -91 2034 -91 \n", "Q 1250 -91 836 529 \n", "Q 422 1150 422 2328 \n", "Q 422 3509 836 4129 \n", "Q 1250 4750 2034 4750 \n", "z\n", "\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-30\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_7\">\n", " <g id=\"line2d_7\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"331.55\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_7\">\n", " <!-- 192 -->\n", " <g transform=\"translate(322.00625 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_8\">\n", " <g id=\"line2d_8\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"380.785294\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_8\">\n", " <!-- 224 -->\n", " <g transform=\"translate(371.241544 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_9\">\n", " <g id=\"line2d_9\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"430.020588\" xlink:href=\"#m088cb034ce\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_9\">\n", " <!-- 256 -->\n", " <g transform=\"translate(420.476838 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 691 4666 \n", "L 3169 4666 \n", "L 3169 4134 \n", "L 1269 4134 \n", "L 1269 2991 \n", "Q 1406 3038 1543 3061 \n", "Q 1681 3084 1819 3084 \n", "Q 2600 3084 3056 2656 \n", "Q 3513 2228 3513 1497 \n", "Q 3513 744 3044 326 \n", "Q 2575 -91 1722 -91 \n", "Q 1428 -91 1123 -41 \n", "Q 819 9 494 109 \n", "L 494 744 \n", "Q 775 591 1075 516 \n", "Q 1375 441 1709 441 \n", "Q 2250 441 2565 725 \n", "Q 2881 1009 2881 1497 \n", "Q 2881 1984 2565 2268 \n", "Q 2250 2553 1709 2553 \n", "Q 1456 2553 1204 2497 \n", "Q 953 2441 691 2322 \n", "L 691 4666 \n", "z\n", "\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-35\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_10\">\n", " <!-- Generation iteration -->\n", " <g transform=\"translate(183.295312 87.99421)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 3809 666 \n", "L 3809 1919 \n", "L 2778 1919 \n", "L 2778 2438 \n", "L 4434 2438 \n", "L 4434 434 \n", "Q 4069 175 3628 42 \n", "Q 3188 -91 2688 -91 \n", "Q 1594 -91 976 548 \n", "Q 359 1188 359 2328 \n", "Q 359 3472 976 4111 \n", "Q 1594 4750 2688 4750 \n", "Q 3144 4750 3555 4637 \n", "Q 3966 4525 4313 4306 \n", "L 4313 3634 \n", "Q 3963 3931 3569 4081 \n", "Q 3175 4231 2741 4231 \n", "Q 1884 4231 1454 3753 \n", "Q 1025 3275 1025 2328 \n", "Q 1025 1384 1454 906 \n", "Q 1884 428 2741 428 \n", "Q 3075 428 3337 486 \n", "Q 3600 544 3809 666 \n", "z\n", "\" id=\"DejaVuSans-47\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1172 4494 \n", "L 1172 3500 \n", "L 2356 3500 \n", "L 2356 3053 \n", "L 1172 3053 \n", "L 1172 1153 \n", "Q 1172 725 1289 603 \n", "Q 1406 481 1766 481 \n", "L 2356 481 \n", "L 2356 0 \n", "L 1766 0 \n", "Q 1100 0 847 248 \n", "Q 594 497 594 1153 \n", "L 594 3053 \n", "L 172 3053 \n", "L 172 3500 \n", "L 594 3500 \n", "L 594 4494 \n", "L 1172 4494 \n", "z\n", "\" id=\"DejaVuSans-74\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-47\"/>\n", " <use x=\"77.490234\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"139.013672\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"202.392578\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"263.916016\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"305.029297\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"366.308594\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"405.517578\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"433.300781\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"494.482422\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"557.861328\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"589.648438\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"617.431641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"656.640625\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"718.164062\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"759.277344\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"820.556641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"859.765625\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"887.548828\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"948.730469\" xlink:href=\"#DejaVuSans-6e\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 59.717647 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 457.1 59.717647 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"p245c227725\">\n", " <rect height=\"52.517647\" width=\"446.4\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 576x576 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"97.273897pt\" version=\"1.1\" viewBox=\"0 0 464.3 97.273897\" width=\"464.3pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:46.488312</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 97.273897 \n", "L 464.3 97.273897 \n", "L 464.3 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "L 457.1 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#p04aa2e7a2b)\">\n", " <image height=\"53\" id=\"imageee1ebb230c\" transform=\"scale(1 -1)translate(0 -53)\" width=\"447\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.717647\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"mc448c0301a\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.138235\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- 1 -->\n", " <g transform=\"translate(32.956985 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 794 531 \n", "L 1825 531 \n", "L 1825 4091 \n", "L 703 3866 \n", "L 703 4441 \n", "L 1819 4666 \n", "L 2450 4666 \n", "L 2450 531 \n", "L 3481 531 \n", "L 3481 0 \n", "L 794 0 \n", "L 794 531 \n", "z\n", "\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"85.373529\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- 32 -->\n", " <g transform=\"translate(79.011029 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2597 2516 \n", "Q 3050 2419 3304 2112 \n", "Q 3559 1806 3559 1356 \n", "Q 3559 666 3084 287 \n", "Q 2609 -91 1734 -91 \n", "Q 1441 -91 1130 -33 \n", "Q 819 25 488 141 \n", "L 488 750 \n", "Q 750 597 1062 519 \n", "Q 1375 441 1716 441 \n", "Q 2309 441 2620 675 \n", "Q 2931 909 2931 1356 \n", "Q 2931 1769 2642 2001 \n", "Q 2353 2234 1838 2234 \n", "L 1294 2234 \n", "L 1294 2753 \n", "L 1863 2753 \n", "Q 2328 2753 2575 2939 \n", "Q 2822 3125 2822 3475 \n", "Q 2822 3834 2567 4026 \n", "Q 2313 4219 1838 4219 \n", "Q 1578 4219 1281 4162 \n", "Q 984 4106 628 3988 \n", "L 628 4550 \n", "Q 988 4650 1302 4700 \n", "Q 1616 4750 1894 4750 \n", "Q 2613 4750 3031 4423 \n", "Q 3450 4097 3450 3541 \n", "Q 3450 3153 3228 2886 \n", "Q 3006 2619 2597 2516 \n", "z\n", "\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1228 531 \n", "L 3431 531 \n", "L 3431 0 \n", "L 469 0 \n", "L 469 531 \n", "Q 828 903 1448 1529 \n", "Q 2069 2156 2228 2338 \n", "Q 2531 2678 2651 2914 \n", "Q 2772 3150 2772 3378 \n", "Q 2772 3750 2511 3984 \n", "Q 2250 4219 1831 4219 \n", "Q 1534 4219 1204 4116 \n", "Q 875 4013 500 3803 \n", "L 500 4441 \n", "Q 881 4594 1212 4672 \n", "Q 1544 4750 1819 4750 \n", "Q 2544 4750 2975 4387 \n", "Q 3406 4025 3406 3419 \n", "Q 3406 3131 3298 2873 \n", "Q 3191 2616 2906 2266 \n", "Q 2828 2175 2409 1742 \n", "Q 1991 1309 1228 531 \n", "z\n", "\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-33\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_3\">\n", " <g id=\"line2d_3\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"134.608824\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_3\">\n", " <!-- 64 -->\n", " <g transform=\"translate(128.246324 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2113 2584 \n", "Q 1688 2584 1439 2293 \n", "Q 1191 2003 1191 1497 \n", "Q 1191 994 1439 701 \n", "Q 1688 409 2113 409 \n", "Q 2538 409 2786 701 \n", "Q 3034 994 3034 1497 \n", "Q 3034 2003 2786 2293 \n", "Q 2538 2584 2113 2584 \n", "z\n", "M 3366 4563 \n", "L 3366 3988 \n", "Q 3128 4100 2886 4159 \n", "Q 2644 4219 2406 4219 \n", "Q 1781 4219 1451 3797 \n", "Q 1122 3375 1075 2522 \n", "Q 1259 2794 1537 2939 \n", "Q 1816 3084 2150 3084 \n", "Q 2853 3084 3261 2657 \n", "Q 3669 2231 3669 1497 \n", "Q 3669 778 3244 343 \n", "Q 2819 -91 2113 -91 \n", "Q 1303 -91 875 529 \n", "Q 447 1150 447 2328 \n", "Q 447 3434 972 4092 \n", "Q 1497 4750 2381 4750 \n", "Q 2619 4750 2861 4703 \n", "Q 3103 4656 3366 4563 \n", "z\n", "\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2419 4116 \n", "L 825 1625 \n", "L 2419 1625 \n", "L 2419 4116 \n", "z\n", "M 2253 4666 \n", "L 3047 4666 \n", "L 3047 1625 \n", "L 3713 1625 \n", "L 3713 1100 \n", "L 3047 1100 \n", "L 3047 0 \n", "L 2419 0 \n", "L 2419 1100 \n", "L 313 1100 \n", "L 313 1709 \n", "L 2253 4666 \n", "z\n", "\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_4\">\n", " <g id=\"line2d_4\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"183.844118\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_4\">\n", " <!-- 96 -->\n", " <g transform=\"translate(177.481618 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 703 97 \n", "L 703 672 \n", "Q 941 559 1184 500 \n", "Q 1428 441 1663 441 \n", "Q 2288 441 2617 861 \n", "Q 2947 1281 2994 2138 \n", "Q 2813 1869 2534 1725 \n", "Q 2256 1581 1919 1581 \n", "Q 1219 1581 811 2004 \n", "Q 403 2428 403 3163 \n", "Q 403 3881 828 4315 \n", "Q 1253 4750 1959 4750 \n", "Q 2769 4750 3195 4129 \n", "Q 3622 3509 3622 2328 \n", "Q 3622 1225 3098 567 \n", "Q 2575 -91 1691 -91 \n", "Q 1453 -91 1209 -44 \n", "Q 966 3 703 97 \n", "z\n", "M 1959 2075 \n", "Q 2384 2075 2632 2365 \n", "Q 2881 2656 2881 3163 \n", "Q 2881 3666 2632 3958 \n", "Q 2384 4250 1959 4250 \n", "Q 1534 4250 1286 3958 \n", "Q 1038 3666 1038 3163 \n", "Q 1038 2656 1286 2365 \n", "Q 1534 2075 1959 2075 \n", "z\n", "\" id=\"DejaVuSans-39\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_5\">\n", " <g id=\"line2d_5\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"233.079412\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_5\">\n", " <!-- 128 -->\n", " <g transform=\"translate(223.535662 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 2216 \n", "Q 1584 2216 1326 1975 \n", "Q 1069 1734 1069 1313 \n", "Q 1069 891 1326 650 \n", "Q 1584 409 2034 409 \n", "Q 2484 409 2743 651 \n", "Q 3003 894 3003 1313 \n", "Q 3003 1734 2745 1975 \n", "Q 2488 2216 2034 2216 \n", "z\n", "M 1403 2484 \n", "Q 997 2584 770 2862 \n", "Q 544 3141 544 3541 \n", "Q 544 4100 942 4425 \n", "Q 1341 4750 2034 4750 \n", "Q 2731 4750 3128 4425 \n", "Q 3525 4100 3525 3541 \n", "Q 3525 3141 3298 2862 \n", "Q 3072 2584 2669 2484 \n", "Q 3125 2378 3379 2068 \n", "Q 3634 1759 3634 1313 \n", "Q 3634 634 3220 271 \n", "Q 2806 -91 2034 -91 \n", "Q 1263 -91 848 271 \n", "Q 434 634 434 1313 \n", "Q 434 1759 690 2068 \n", "Q 947 2378 1403 2484 \n", "z\n", "M 1172 3481 \n", "Q 1172 3119 1398 2916 \n", "Q 1625 2713 2034 2713 \n", "Q 2441 2713 2670 2916 \n", "Q 2900 3119 2900 3481 \n", "Q 2900 3844 2670 4047 \n", "Q 2441 4250 2034 4250 \n", "Q 1625 4250 1398 4047 \n", "Q 1172 3844 1172 3481 \n", "z\n", "\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-38\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_6\">\n", " <g id=\"line2d_6\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.314706\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_6\">\n", " <!-- 160 -->\n", " <g transform=\"translate(272.770956 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 4250 \n", "Q 1547 4250 1301 3770 \n", "Q 1056 3291 1056 2328 \n", "Q 1056 1369 1301 889 \n", "Q 1547 409 2034 409 \n", "Q 2525 409 2770 889 \n", "Q 3016 1369 3016 2328 \n", "Q 3016 3291 2770 3770 \n", "Q 2525 4250 2034 4250 \n", "z\n", "M 2034 4750 \n", "Q 2819 4750 3233 4129 \n", "Q 3647 3509 3647 2328 \n", "Q 3647 1150 3233 529 \n", "Q 2819 -91 2034 -91 \n", "Q 1250 -91 836 529 \n", "Q 422 1150 422 2328 \n", "Q 422 3509 836 4129 \n", "Q 1250 4750 2034 4750 \n", "z\n", "\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-30\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_7\">\n", " <g id=\"line2d_7\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"331.55\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_7\">\n", " <!-- 192 -->\n", " <g transform=\"translate(322.00625 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_8\">\n", " <g id=\"line2d_8\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"380.785294\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_8\">\n", " <!-- 224 -->\n", " <g transform=\"translate(371.241544 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_9\">\n", " <g id=\"line2d_9\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"430.020588\" xlink:href=\"#mc448c0301a\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_9\">\n", " <!-- 256 -->\n", " <g transform=\"translate(420.476838 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 691 4666 \n", "L 3169 4666 \n", "L 3169 4134 \n", "L 1269 4134 \n", "L 1269 2991 \n", "Q 1406 3038 1543 3061 \n", "Q 1681 3084 1819 3084 \n", "Q 2600 3084 3056 2656 \n", "Q 3513 2228 3513 1497 \n", "Q 3513 744 3044 326 \n", "Q 2575 -91 1722 -91 \n", "Q 1428 -91 1123 -41 \n", "Q 819 9 494 109 \n", "L 494 744 \n", "Q 775 591 1075 516 \n", "Q 1375 441 1709 441 \n", "Q 2250 441 2565 725 \n", "Q 2881 1009 2881 1497 \n", "Q 2881 1984 2565 2268 \n", "Q 2250 2553 1709 2553 \n", "Q 1456 2553 1204 2497 \n", "Q 953 2441 691 2322 \n", "L 691 4666 \n", "z\n", "\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-35\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_10\">\n", " <!-- Generation iteration -->\n", " <g transform=\"translate(183.295312 87.99421)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 3809 666 \n", "L 3809 1919 \n", "L 2778 1919 \n", "L 2778 2438 \n", "L 4434 2438 \n", "L 4434 434 \n", "Q 4069 175 3628 42 \n", "Q 3188 -91 2688 -91 \n", "Q 1594 -91 976 548 \n", "Q 359 1188 359 2328 \n", "Q 359 3472 976 4111 \n", "Q 1594 4750 2688 4750 \n", "Q 3144 4750 3555 4637 \n", "Q 3966 4525 4313 4306 \n", "L 4313 3634 \n", "Q 3963 3931 3569 4081 \n", "Q 3175 4231 2741 4231 \n", "Q 1884 4231 1454 3753 \n", "Q 1025 3275 1025 2328 \n", "Q 1025 1384 1454 906 \n", "Q 1884 428 2741 428 \n", "Q 3075 428 3337 486 \n", "Q 3600 544 3809 666 \n", "z\n", "\" id=\"DejaVuSans-47\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1172 4494 \n", "L 1172 3500 \n", "L 2356 3500 \n", "L 2356 3053 \n", "L 1172 3053 \n", "L 1172 1153 \n", "Q 1172 725 1289 603 \n", "Q 1406 481 1766 481 \n", "L 2356 481 \n", "L 2356 0 \n", "L 1766 0 \n", "Q 1100 0 847 248 \n", "Q 594 497 594 1153 \n", "L 594 3053 \n", "L 172 3053 \n", "L 172 3500 \n", "L 594 3500 \n", "L 594 4494 \n", "L 1172 4494 \n", "z\n", "\" id=\"DejaVuSans-74\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-47\"/>\n", " <use x=\"77.490234\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"139.013672\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"202.392578\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"263.916016\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"305.029297\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"366.308594\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"405.517578\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"433.300781\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"494.482422\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"557.861328\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"589.648438\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"617.431641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"656.640625\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"718.164062\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"759.277344\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"820.556641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"859.765625\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"887.548828\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"948.730469\" xlink:href=\"#DejaVuSans-6e\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 59.717647 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 457.1 59.717647 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"p04aa2e7a2b\">\n", " <rect height=\"52.517647\" width=\"446.4\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 576x576 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"97.273897pt\" version=\"1.1\" viewBox=\"0 0 464.3 97.273897\" width=\"464.3pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:46.639358</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 97.273897 \n", "L 464.3 97.273897 \n", "L 464.3 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "L 457.1 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#p7c1d101b24)\">\n", " <image height=\"53\" id=\"image6d18cb3302\" transform=\"scale(1 -1)translate(0 -53)\" width=\"447\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.717647\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"m9a16802fcd\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.138235\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- 1 -->\n", " <g transform=\"translate(32.956985 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 794 531 \n", "L 1825 531 \n", "L 1825 4091 \n", "L 703 3866 \n", "L 703 4441 \n", "L 1819 4666 \n", "L 2450 4666 \n", "L 2450 531 \n", "L 3481 531 \n", "L 3481 0 \n", "L 794 0 \n", "L 794 531 \n", "z\n", "\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"85.373529\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- 32 -->\n", " <g transform=\"translate(79.011029 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2597 2516 \n", "Q 3050 2419 3304 2112 \n", "Q 3559 1806 3559 1356 \n", "Q 3559 666 3084 287 \n", "Q 2609 -91 1734 -91 \n", "Q 1441 -91 1130 -33 \n", "Q 819 25 488 141 \n", "L 488 750 \n", "Q 750 597 1062 519 \n", "Q 1375 441 1716 441 \n", "Q 2309 441 2620 675 \n", "Q 2931 909 2931 1356 \n", "Q 2931 1769 2642 2001 \n", "Q 2353 2234 1838 2234 \n", "L 1294 2234 \n", "L 1294 2753 \n", "L 1863 2753 \n", "Q 2328 2753 2575 2939 \n", "Q 2822 3125 2822 3475 \n", "Q 2822 3834 2567 4026 \n", "Q 2313 4219 1838 4219 \n", "Q 1578 4219 1281 4162 \n", "Q 984 4106 628 3988 \n", "L 628 4550 \n", "Q 988 4650 1302 4700 \n", "Q 1616 4750 1894 4750 \n", "Q 2613 4750 3031 4423 \n", "Q 3450 4097 3450 3541 \n", "Q 3450 3153 3228 2886 \n", "Q 3006 2619 2597 2516 \n", "z\n", "\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1228 531 \n", "L 3431 531 \n", "L 3431 0 \n", "L 469 0 \n", "L 469 531 \n", "Q 828 903 1448 1529 \n", "Q 2069 2156 2228 2338 \n", "Q 2531 2678 2651 2914 \n", "Q 2772 3150 2772 3378 \n", "Q 2772 3750 2511 3984 \n", "Q 2250 4219 1831 4219 \n", "Q 1534 4219 1204 4116 \n", "Q 875 4013 500 3803 \n", "L 500 4441 \n", "Q 881 4594 1212 4672 \n", "Q 1544 4750 1819 4750 \n", "Q 2544 4750 2975 4387 \n", "Q 3406 4025 3406 3419 \n", "Q 3406 3131 3298 2873 \n", "Q 3191 2616 2906 2266 \n", "Q 2828 2175 2409 1742 \n", "Q 1991 1309 1228 531 \n", "z\n", "\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-33\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_3\">\n", " <g id=\"line2d_3\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"134.608824\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_3\">\n", " <!-- 64 -->\n", " <g transform=\"translate(128.246324 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2113 2584 \n", "Q 1688 2584 1439 2293 \n", "Q 1191 2003 1191 1497 \n", "Q 1191 994 1439 701 \n", "Q 1688 409 2113 409 \n", "Q 2538 409 2786 701 \n", "Q 3034 994 3034 1497 \n", "Q 3034 2003 2786 2293 \n", "Q 2538 2584 2113 2584 \n", "z\n", "M 3366 4563 \n", "L 3366 3988 \n", "Q 3128 4100 2886 4159 \n", "Q 2644 4219 2406 4219 \n", "Q 1781 4219 1451 3797 \n", "Q 1122 3375 1075 2522 \n", "Q 1259 2794 1537 2939 \n", "Q 1816 3084 2150 3084 \n", "Q 2853 3084 3261 2657 \n", "Q 3669 2231 3669 1497 \n", "Q 3669 778 3244 343 \n", "Q 2819 -91 2113 -91 \n", "Q 1303 -91 875 529 \n", "Q 447 1150 447 2328 \n", "Q 447 3434 972 4092 \n", "Q 1497 4750 2381 4750 \n", "Q 2619 4750 2861 4703 \n", "Q 3103 4656 3366 4563 \n", "z\n", "\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2419 4116 \n", "L 825 1625 \n", "L 2419 1625 \n", "L 2419 4116 \n", "z\n", "M 2253 4666 \n", "L 3047 4666 \n", "L 3047 1625 \n", "L 3713 1625 \n", "L 3713 1100 \n", "L 3047 1100 \n", "L 3047 0 \n", "L 2419 0 \n", "L 2419 1100 \n", "L 313 1100 \n", "L 313 1709 \n", "L 2253 4666 \n", "z\n", "\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_4\">\n", " <g id=\"line2d_4\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"183.844118\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_4\">\n", " <!-- 96 -->\n", " <g transform=\"translate(177.481618 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 703 97 \n", "L 703 672 \n", "Q 941 559 1184 500 \n", "Q 1428 441 1663 441 \n", "Q 2288 441 2617 861 \n", "Q 2947 1281 2994 2138 \n", "Q 2813 1869 2534 1725 \n", "Q 2256 1581 1919 1581 \n", "Q 1219 1581 811 2004 \n", "Q 403 2428 403 3163 \n", "Q 403 3881 828 4315 \n", "Q 1253 4750 1959 4750 \n", "Q 2769 4750 3195 4129 \n", "Q 3622 3509 3622 2328 \n", "Q 3622 1225 3098 567 \n", "Q 2575 -91 1691 -91 \n", "Q 1453 -91 1209 -44 \n", "Q 966 3 703 97 \n", "z\n", "M 1959 2075 \n", "Q 2384 2075 2632 2365 \n", "Q 2881 2656 2881 3163 \n", "Q 2881 3666 2632 3958 \n", "Q 2384 4250 1959 4250 \n", "Q 1534 4250 1286 3958 \n", "Q 1038 3666 1038 3163 \n", "Q 1038 2656 1286 2365 \n", "Q 1534 2075 1959 2075 \n", "z\n", "\" id=\"DejaVuSans-39\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_5\">\n", " <g id=\"line2d_5\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"233.079412\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_5\">\n", " <!-- 128 -->\n", " <g transform=\"translate(223.535662 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 2216 \n", "Q 1584 2216 1326 1975 \n", "Q 1069 1734 1069 1313 \n", "Q 1069 891 1326 650 \n", "Q 1584 409 2034 409 \n", "Q 2484 409 2743 651 \n", "Q 3003 894 3003 1313 \n", "Q 3003 1734 2745 1975 \n", "Q 2488 2216 2034 2216 \n", "z\n", "M 1403 2484 \n", "Q 997 2584 770 2862 \n", "Q 544 3141 544 3541 \n", "Q 544 4100 942 4425 \n", "Q 1341 4750 2034 4750 \n", "Q 2731 4750 3128 4425 \n", "Q 3525 4100 3525 3541 \n", "Q 3525 3141 3298 2862 \n", "Q 3072 2584 2669 2484 \n", "Q 3125 2378 3379 2068 \n", "Q 3634 1759 3634 1313 \n", "Q 3634 634 3220 271 \n", "Q 2806 -91 2034 -91 \n", "Q 1263 -91 848 271 \n", "Q 434 634 434 1313 \n", "Q 434 1759 690 2068 \n", "Q 947 2378 1403 2484 \n", "z\n", "M 1172 3481 \n", "Q 1172 3119 1398 2916 \n", "Q 1625 2713 2034 2713 \n", "Q 2441 2713 2670 2916 \n", "Q 2900 3119 2900 3481 \n", "Q 2900 3844 2670 4047 \n", "Q 2441 4250 2034 4250 \n", "Q 1625 4250 1398 4047 \n", "Q 1172 3844 1172 3481 \n", "z\n", "\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-38\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_6\">\n", " <g id=\"line2d_6\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.314706\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_6\">\n", " <!-- 160 -->\n", " <g transform=\"translate(272.770956 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2034 4250 \n", "Q 1547 4250 1301 3770 \n", "Q 1056 3291 1056 2328 \n", "Q 1056 1369 1301 889 \n", "Q 1547 409 2034 409 \n", "Q 2525 409 2770 889 \n", "Q 3016 1369 3016 2328 \n", "Q 3016 3291 2770 3770 \n", "Q 2525 4250 2034 4250 \n", "z\n", "M 2034 4750 \n", "Q 2819 4750 3233 4129 \n", "Q 3647 3509 3647 2328 \n", "Q 3647 1150 3233 529 \n", "Q 2819 -91 2034 -91 \n", "Q 1250 -91 836 529 \n", "Q 422 1150 422 2328 \n", "Q 422 3509 836 4129 \n", "Q 1250 4750 2034 4750 \n", "z\n", "\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-36\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-30\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_7\">\n", " <g id=\"line2d_7\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"331.55\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_7\">\n", " <!-- 192 -->\n", " <g transform=\"translate(322.00625 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-31\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-39\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-32\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_8\">\n", " <g id=\"line2d_8\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"380.785294\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_8\">\n", " <!-- 224 -->\n", " <g transform=\"translate(371.241544 74.316085)scale(0.1 -0.1)\">\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-34\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_9\">\n", " <g id=\"line2d_9\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"430.020588\" xlink:href=\"#m9a16802fcd\" y=\"59.717647\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_9\">\n", " <!-- 256 -->\n", " <g transform=\"translate(420.476838 74.316085)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 691 4666 \n", "L 3169 4666 \n", "L 3169 4134 \n", "L 1269 4134 \n", "L 1269 2991 \n", "Q 1406 3038 1543 3061 \n", "Q 1681 3084 1819 3084 \n", "Q 2600 3084 3056 2656 \n", "Q 3513 2228 3513 1497 \n", "Q 3513 744 3044 326 \n", "Q 2575 -91 1722 -91 \n", "Q 1428 -91 1123 -41 \n", "Q 819 9 494 109 \n", "L 494 744 \n", "Q 775 591 1075 516 \n", "Q 1375 441 1709 441 \n", "Q 2250 441 2565 725 \n", "Q 2881 1009 2881 1497 \n", "Q 2881 1984 2565 2268 \n", "Q 2250 2553 1709 2553 \n", "Q 1456 2553 1204 2497 \n", "Q 953 2441 691 2322 \n", "L 691 4666 \n", "z\n", "\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-32\"/>\n", " <use x=\"63.623047\" xlink:href=\"#DejaVuSans-35\"/>\n", " <use x=\"127.246094\" xlink:href=\"#DejaVuSans-36\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_10\">\n", " <!-- Generation iteration -->\n", " <g transform=\"translate(183.295312 87.99421)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 3809 666 \n", "L 3809 1919 \n", "L 2778 1919 \n", "L 2778 2438 \n", "L 4434 2438 \n", "L 4434 434 \n", "Q 4069 175 3628 42 \n", "Q 3188 -91 2688 -91 \n", "Q 1594 -91 976 548 \n", "Q 359 1188 359 2328 \n", "Q 359 3472 976 4111 \n", "Q 1594 4750 2688 4750 \n", "Q 3144 4750 3555 4637 \n", "Q 3966 4525 4313 4306 \n", "L 4313 3634 \n", "Q 3963 3931 3569 4081 \n", "Q 3175 4231 2741 4231 \n", "Q 1884 4231 1454 3753 \n", "Q 1025 3275 1025 2328 \n", "Q 1025 1384 1454 906 \n", "Q 1884 428 2741 428 \n", "Q 3075 428 3337 486 \n", "Q 3600 544 3809 666 \n", "z\n", "\" id=\"DejaVuSans-47\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1172 4494 \n", "L 1172 3500 \n", "L 2356 3500 \n", "L 2356 3053 \n", "L 1172 3053 \n", "L 1172 1153 \n", "Q 1172 725 1289 603 \n", "Q 1406 481 1766 481 \n", "L 2356 481 \n", "L 2356 0 \n", "L 1766 0 \n", "Q 1100 0 847 248 \n", "Q 594 497 594 1153 \n", "L 594 3053 \n", "L 172 3053 \n", "L 172 3500 \n", "L 594 3500 \n", "L 594 4494 \n", "L 1172 4494 \n", "z\n", "\" id=\"DejaVuSans-74\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-47\"/>\n", " <use x=\"77.490234\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"139.013672\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"202.392578\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"263.916016\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"305.029297\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"366.308594\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"405.517578\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"433.300781\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"494.482422\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"557.861328\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"589.648438\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"617.431641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"656.640625\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"718.164062\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"759.277344\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"820.556641\" xlink:href=\"#DejaVuSans-74\"/>\n", " <use x=\"859.765625\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"887.548828\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"948.730469\" xlink:href=\"#DejaVuSans-6e\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 59.717647 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 457.1 59.717647 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 59.717647 \n", "L 457.1 59.717647 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 457.1 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"p7c1d101b24\">\n", " <rect height=\"52.517647\" width=\"446.4\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 576x576 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["for i in range(imgs_per_step.shape[1]):\n", " step_size = callback.num_steps // callback.vis_steps\n", " imgs_to_plot = imgs_per_step[step_size - 1 :: step_size, i]\n", " imgs_to_plot = torch.cat([imgs_per_step[0:1, i], imgs_to_plot], dim=0)\n", " grid = torchvision.utils.make_grid(\n", " imgs_to_plot, nrow=imgs_to_plot.shape[0], normalize=True, range=(-1, 1), pad_value=0.5, padding=2\n", " )\n", " grid = grid.permute(1, 2, 0)\n", " plt.figure(figsize=(8, 8))\n", " plt.imshow(grid)\n", " plt.xlabel(\"Generation iteration\")\n", " plt.xticks(\n", " [(imgs_per_step.shape[-1] + 2) * (0.5 + j) for j in range(callback.vis_steps + 1)],\n", " labels=[1] + list(range(step_size, imgs_per_step.shape[0] + 1, step_size)),\n", " )\n", " plt.yticks([])\n", " plt.show()"]}, {"cell_type": "markdown", "id": "d85bacf3", "metadata": {"papermill": {"duration": 0.032666, "end_time": "2021-09-16T12:40:46.804930", "exception": false, "start_time": "2021-09-16T12:40:46.772264", "status": "completed"}, "tags": []}, "source": ["We see that although starting from noise in the very first step, the sampling algorithm obtains reasonable shapes after only 32 steps.\n", "Over the next 200 steps, the shapes become clearer and changed towards realistic digits.\n", "The specific samples can differ when you run the code on Colab, hence the following description is specific to the plots shown on the website.\n", "The first row shows an 8, where we remove unnecessary white parts over iterations.\n", "The transformation across iterations can be seen at best for the second sample, which creates a digit of 2.\n", "While the first sample after 32 iterations looks a bit like a digit, but not really,\n", "the sample is transformed more and more to a typical image of the digit 2."]}, {"cell_type": "markdown", "id": "9b5682ed", "metadata": {"papermill": {"duration": 0.03313, "end_time": "2021-09-16T12:40:46.870416", "exception": false, "start_time": "2021-09-16T12:40:46.837286", "status": "completed"}, "tags": []}, "source": ["### Out-of-distribution detection\n", "\n", "A very common and strong application of energy-based models is out-of-distribution detection\n", "(sometimes referred to as \"anomaly\" detection).\n", "As more and more deep learning models are applied in production and applications,\n", "a crucial aspect of these models is to know what the models don't know.\n", "Deep learning models are usually overconfident, meaning that they classify even random images sometimes with 100% probability.\n", "Clearly, this is not something that we want to see in applications.\n", "Energy-based models can help with this problem because they are trained to detect images that do not fit the training dataset distribution.\n", "Thus, in those applications, you could train an energy-based model along with the classifier,\n", "and only output predictions if the energy-based models assign a (unnormalized) probability higher than $\\delta$ to the image.\n", "You can actually combine classifiers and energy-based objectives in a single model,\n", "as proposed in this [paper](https://arxiv.org/abs/1912.03263).\n", "\n", "In this part of the analysis, we want to test the out-of-distribution capability of our energy-based model.\n", "Remember that a lower output of the model denotes a low probability.\n", "Thus, we hope to see low scores if we enter random noise to the model:"]}, {"cell_type": "code", "execution_count": 16, "id": "303c00f7", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:46.941073Z", "iopub.status.busy": "2021-09-16T12:40:46.940608Z", "iopub.status.idle": "2021-09-16T12:40:46.945276Z", "shell.execute_reply": "2021-09-16T12:40:46.944875Z"}, "papermill": {"duration": 0.041937, "end_time": "2021-09-16T12:40:46.945424", "exception": false, "start_time": "2021-09-16T12:40:46.903487", "status": "completed"}, "tags": []}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Average score for random images: -17.88\n"]}], "source": ["with torch.no_grad():\n", " rand_imgs = torch.rand((128,) + model.hparams.img_shape).to(model.device)\n", " rand_imgs = rand_imgs * 2 - 1.0\n", " rand_out = model.cnn(rand_imgs).mean()\n", " print(\"Average score for random images: %4.2f\" % (rand_out.item()))"]}, {"cell_type": "markdown", "id": "0a485fdb", "metadata": {"papermill": {"duration": 0.032686, "end_time": "2021-09-16T12:40:47.012111", "exception": false, "start_time": "2021-09-16T12:40:46.979425", "status": "completed"}, "tags": []}, "source": ["As we hoped, the model assigns very low probability to those noisy images.\n", "As another reference, let's look at predictions for a batch of images from the training set:"]}, {"cell_type": "code", "execution_count": 17, "id": "2bcb1282", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:47.081066Z", "iopub.status.busy": "2021-09-16T12:40:47.080584Z", "iopub.status.idle": "2021-09-16T12:40:47.233910Z", "shell.execute_reply": "2021-09-16T12:40:47.233401Z"}, "papermill": {"duration": 0.189477, "end_time": "2021-09-16T12:40:47.234026", "exception": false, "start_time": "2021-09-16T12:40:47.044549", "status": "completed"}, "tags": []}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Average score for training images: -0.00\n"]}], "source": ["with torch.no_grad():\n", " train_imgs, _ = next(iter(train_loader))\n", " train_imgs = train_imgs.to(model.device)\n", " train_out = model.cnn(train_imgs).mean()\n", " print(\"Average score for training images: %4.2f\" % (train_out.item()))"]}, {"cell_type": "markdown", "id": "a559009f", "metadata": {"lines_to_next_cell": 2, "papermill": {"duration": 0.032727, "end_time": "2021-09-16T12:40:47.300644", "exception": false, "start_time": "2021-09-16T12:40:47.267917", "status": "completed"}, "tags": []}, "source": ["The scores are close to 0 because of the regularization objective that was added to the training.\n", "So clearly, the model can distinguish between noise and real digits.\n", "However, what happens if we change the training images a little, and see which ones gets a very low score?"]}, {"cell_type": "code", "execution_count": 18, "id": "edff6bb0", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:47.372822Z", "iopub.status.busy": "2021-09-16T12:40:47.372352Z", "iopub.status.idle": "2021-09-16T12:40:47.374505Z", "shell.execute_reply": "2021-09-16T12:40:47.374110Z"}, "papermill": {"duration": 0.041215, "end_time": "2021-09-16T12:40:47.374604", "exception": false, "start_time": "2021-09-16T12:40:47.333389", "status": "completed"}, "tags": []}, "outputs": [], "source": ["@torch.no_grad()\n", "def compare_images(img1, img2):\n", " imgs = torch.stack([img1, img2], dim=0).to(model.device)\n", " score1, score2 = model.cnn(imgs).cpu().chunk(2, dim=0)\n", " grid = torchvision.utils.make_grid(\n", " [img1.cpu(), img2.cpu()], nrow=2, normalize=True, range=(-1, 1), pad_value=0.5, padding=2\n", " )\n", " grid = grid.permute(1, 2, 0)\n", " plt.figure(figsize=(4, 4))\n", " plt.imshow(grid)\n", " plt.xticks([(img1.shape[2] + 2) * (0.5 + j) for j in range(2)], labels=[\"Original image\", \"Transformed image\"])\n", " plt.yticks([])\n", " plt.show()\n", " print(\"Score original image: %4.2f\" % score1)\n", " print(\"Score transformed image: %4.2f\" % score2)"]}, {"cell_type": "markdown", "id": "7c540cbd", "metadata": {"papermill": {"duration": 0.033108, "end_time": "2021-09-16T12:40:47.440512", "exception": false, "start_time": "2021-09-16T12:40:47.407404", "status": "completed"}, "tags": []}, "source": ["We use a random test image for this. Feel free to change it to experiment with the model yourself."]}, {"cell_type": "code", "execution_count": 19, "id": "befba0f4", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:47.509319Z", "iopub.status.busy": "2021-09-16T12:40:47.508856Z", "iopub.status.idle": "2021-09-16T12:40:47.685776Z", "shell.execute_reply": "2021-09-16T12:40:47.686151Z"}, "papermill": {"duration": 0.212897, "end_time": "2021-09-16T12:40:47.686303", "exception": false, "start_time": "2021-09-16T12:40:47.473406", "status": "completed"}, "tags": []}, "outputs": [], "source": ["test_imgs, _ = next(iter(test_loader))\n", "exmp_img = test_imgs[0].to(model.device)"]}, {"cell_type": "markdown", "id": "12364d29", "metadata": {"papermill": {"duration": 0.033603, "end_time": "2021-09-16T12:40:47.754499", "exception": false, "start_time": "2021-09-16T12:40:47.720896", "status": "completed"}, "tags": []}, "source": ["The first transformation is to add some random noise to the image:"]}, {"cell_type": "code", "execution_count": 20, "id": "bc21923d", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:47.824609Z", "iopub.status.busy": "2021-09-16T12:40:47.824143Z", "iopub.status.idle": "2021-09-16T12:40:47.919759Z", "shell.execute_reply": "2021-09-16T12:40:47.919292Z"}, "papermill": {"duration": 0.132328, "end_time": "2021-09-16T12:40:47.919863", "exception": false, "start_time": "2021-09-16T12:40:47.787535", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"146.278125pt\" version=\"1.1\" viewBox=\"0 0 241.1 146.278125\" width=\"241.1pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:47.862252</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 146.278125 \n", "L 241.1 146.278125 \n", "L 241.1 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "L 233.9 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#p98e7d7e533)\">\n", " <image height=\"116\" id=\"image0eb6a61bde\" transform=\"scale(1 -1)translate(0 -116)\" width=\"224\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.4\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"m23b9680fb7\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"66.5\" xlink:href=\"#m23b9680fb7\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- Original image -->\n", " <g transform=\"translate(29.771094 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2522 4238 \n", "Q 1834 4238 1429 3725 \n", "Q 1025 3213 1025 2328 \n", "Q 1025 1447 1429 934 \n", "Q 1834 422 2522 422 \n", "Q 3209 422 3611 934 \n", "Q 4013 1447 4013 2328 \n", "Q 4013 3213 3611 3725 \n", "Q 3209 4238 2522 4238 \n", "z\n", "M 2522 4750 \n", "Q 3503 4750 4090 4092 \n", "Q 4678 3434 4678 2328 \n", "Q 4678 1225 4090 567 \n", "Q 3503 -91 2522 -91 \n", "Q 1538 -91 948 565 \n", "Q 359 1222 359 2328 \n", "Q 359 3434 948 4092 \n", "Q 1538 4750 2522 4750 \n", "z\n", "\" id=\"DejaVuSans-4f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 1791 \n", "Q 2906 2416 2648 2759 \n", "Q 2391 3103 1925 3103 \n", "Q 1463 3103 1205 2759 \n", "Q 947 2416 947 1791 \n", "Q 947 1169 1205 825 \n", "Q 1463 481 1925 481 \n", "Q 2391 481 2648 825 \n", "Q 2906 1169 2906 1791 \n", "z\n", "M 3481 434 \n", "Q 3481 -459 3084 -895 \n", "Q 2688 -1331 1869 -1331 \n", "Q 1566 -1331 1297 -1286 \n", "Q 1028 -1241 775 -1147 \n", "L 775 -588 \n", "Q 1028 -725 1275 -790 \n", "Q 1522 -856 1778 -856 \n", "Q 2344 -856 2625 -561 \n", "Q 2906 -266 2906 331 \n", "L 2906 616 \n", "Q 2728 306 2450 153 \n", "Q 2172 0 1784 0 \n", "Q 1141 0 747 490 \n", "Q 353 981 353 1791 \n", "Q 353 2603 747 3093 \n", "Q 1141 3584 1784 3584 \n", "Q 2172 3584 2450 3431 \n", "Q 2728 3278 2906 2969 \n", "L 2906 3500 \n", "L 3481 3500 \n", "L 3481 434 \n", "z\n", "\" id=\"DejaVuSans-67\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 4863 \n", "L 1178 4863 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-6c\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3328 2828 \n", "Q 3544 3216 3844 3400 \n", "Q 4144 3584 4550 3584 \n", "Q 5097 3584 5394 3201 \n", "Q 5691 2819 5691 2113 \n", "L 5691 0 \n", "L 5113 0 \n", "L 5113 2094 \n", "Q 5113 2597 4934 2840 \n", "Q 4756 3084 4391 3084 \n", "Q 3944 3084 3684 2787 \n", "Q 3425 2491 3425 1978 \n", "L 3425 0 \n", "L 2847 0 \n", "L 2847 2094 \n", "Q 2847 2600 2669 2842 \n", "Q 2491 3084 2119 3084 \n", "Q 1678 3084 1418 2786 \n", "Q 1159 2488 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1356 3278 1631 3431 \n", "Q 1906 3584 2284 3584 \n", "Q 2666 3584 2933 3390 \n", "Q 3200 3197 3328 2828 \n", "z\n", "\" id=\"DejaVuSans-6d\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-4f\"/>\n", " <use x=\"78.710938\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"119.824219\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"147.607422\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"211.083984\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"238.867188\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"302.246094\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"363.525391\" xlink:href=\"#DejaVuSans-6c\"/>\n", " <use x=\"391.308594\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"423.095703\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"450.878906\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"548.291016\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"609.570312\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"673.046875\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"174.5\" xlink:href=\"#m23b9680fb7\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- Transformed image -->\n", " <g transform=\"translate(126.21875 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M -19 4666 \n", "L 3928 4666 \n", "L 3928 4134 \n", "L 2272 4134 \n", "L 2272 0 \n", "L 1638 0 \n", "L 1638 4134 \n", "L -19 4134 \n", "L -19 4666 \n", "z\n", "\" id=\"DejaVuSans-54\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2834 3397 \n", "L 2834 2853 \n", "Q 2591 2978 2328 3040 \n", "Q 2066 3103 1784 3103 \n", "Q 1356 3103 1142 2972 \n", "Q 928 2841 928 2578 \n", "Q 928 2378 1081 2264 \n", "Q 1234 2150 1697 2047 \n", "L 1894 2003 \n", "Q 2506 1872 2764 1633 \n", "Q 3022 1394 3022 966 \n", "Q 3022 478 2636 193 \n", "Q 2250 -91 1575 -91 \n", "Q 1294 -91 989 -36 \n", "Q 684 19 347 128 \n", "L 347 722 \n", "Q 666 556 975 473 \n", "Q 1284 391 1588 391 \n", "Q 1994 391 2212 530 \n", "Q 2431 669 2431 922 \n", "Q 2431 1156 2273 1281 \n", "Q 2116 1406 1581 1522 \n", "L 1381 1569 \n", "Q 847 1681 609 1914 \n", "Q 372 2147 372 2553 \n", "Q 372 3047 722 3315 \n", "Q 1072 3584 1716 3584 \n", "Q 2034 3584 2315 3537 \n", "Q 2597 3491 2834 3397 \n", "z\n", "\" id=\"DejaVuSans-73\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2375 4863 \n", "L 2375 4384 \n", "L 1825 4384 \n", "Q 1516 4384 1395 4259 \n", "Q 1275 4134 1275 3809 \n", "L 1275 3500 \n", "L 2222 3500 \n", "L 2222 3053 \n", "L 1275 3053 \n", "L 1275 0 \n", "L 697 0 \n", "L 697 3053 \n", "L 147 3053 \n", "L 147 3500 \n", "L 697 3500 \n", "L 697 3744 \n", "Q 697 4328 969 4595 \n", "Q 1241 4863 1831 4863 \n", "L 2375 4863 \n", "z\n", "\" id=\"DejaVuSans-66\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 2969 \n", "L 2906 4863 \n", "L 3481 4863 \n", "L 3481 0 \n", "L 2906 0 \n", "L 2906 525 \n", "Q 2725 213 2448 61 \n", "Q 2172 -91 1784 -91 \n", "Q 1150 -91 751 415 \n", "Q 353 922 353 1747 \n", "Q 353 2572 751 3078 \n", "Q 1150 3584 1784 3584 \n", "Q 2172 3584 2448 3432 \n", "Q 2725 3281 2906 2969 \n", "z\n", "M 947 1747 \n", "Q 947 1113 1208 752 \n", "Q 1469 391 1925 391 \n", "Q 2381 391 2643 752 \n", "Q 2906 1113 2906 1747 \n", "Q 2906 2381 2643 2742 \n", "Q 2381 3103 1925 3103 \n", "Q 1469 3103 1208 2742 \n", "Q 947 2381 947 1747 \n", "z\n", "\" id=\"DejaVuSans-64\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-54\"/>\n", " <use x=\"46.333984\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"87.447266\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"148.726562\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"212.105469\" xlink:href=\"#DejaVuSans-73\"/>\n", " <use x=\"264.205078\" xlink:href=\"#DejaVuSans-66\"/>\n", " <use x=\"299.410156\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"360.591797\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"399.955078\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"497.367188\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"558.890625\" xlink:href=\"#DejaVuSans-64\"/>\n", " <use x=\"622.367188\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"654.154297\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"681.9375\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"779.349609\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"840.628906\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"904.105469\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 122.4 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 233.9 122.4 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"p98e7d7e533\">\n", " <rect height=\"115.2\" width=\"223.2\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 288x288 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stdout", "output_type": "stream", "text": ["Score original image: 0.03\n", "Score transformed image: -0.07\n"]}], "source": ["img_noisy = exmp_img + torch.randn_like(exmp_img) * 0.3\n", "img_noisy.clamp_(min=-1.0, max=1.0)\n", "compare_images(exmp_img, img_noisy)"]}, {"cell_type": "markdown", "id": "2544f964", "metadata": {"papermill": {"duration": 0.03459, "end_time": "2021-09-16T12:40:47.989386", "exception": false, "start_time": "2021-09-16T12:40:47.954796", "status": "completed"}, "tags": []}, "source": ["We can see that the score considerably drops.\n", "Hence, the model can detect random Gaussian noise on the image.\n", "This is also to expect as initially, the \"fake\" samples are pure noise images.\n", "\n", "Next, we flip an image and check how this influences the score:"]}, {"cell_type": "code", "execution_count": 21, "id": "cc6e4e18", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:48.060789Z", "iopub.status.busy": "2021-09-16T12:40:48.060321Z", "iopub.status.idle": "2021-09-16T12:40:48.147462Z", "shell.execute_reply": "2021-09-16T12:40:48.147064Z"}, "papermill": {"duration": 0.12397, "end_time": "2021-09-16T12:40:48.147562", "exception": false, "start_time": "2021-09-16T12:40:48.023592", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"146.278125pt\" version=\"1.1\" viewBox=\"0 0 241.1 146.278125\" width=\"241.1pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:48.094457</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 146.278125 \n", "L 241.1 146.278125 \n", "L 241.1 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "L 233.9 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#p32235d7fcf)\">\n", " <image height=\"116\" id=\"image7773599031\" transform=\"scale(1 -1)translate(0 -116)\" width=\"224\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.4\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"mbb074bbc39\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"66.5\" xlink:href=\"#mbb074bbc39\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- Original image -->\n", " <g transform=\"translate(29.771094 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2522 4238 \n", "Q 1834 4238 1429 3725 \n", "Q 1025 3213 1025 2328 \n", "Q 1025 1447 1429 934 \n", "Q 1834 422 2522 422 \n", "Q 3209 422 3611 934 \n", "Q 4013 1447 4013 2328 \n", "Q 4013 3213 3611 3725 \n", "Q 3209 4238 2522 4238 \n", "z\n", "M 2522 4750 \n", "Q 3503 4750 4090 4092 \n", "Q 4678 3434 4678 2328 \n", "Q 4678 1225 4090 567 \n", "Q 3503 -91 2522 -91 \n", "Q 1538 -91 948 565 \n", "Q 359 1222 359 2328 \n", "Q 359 3434 948 4092 \n", "Q 1538 4750 2522 4750 \n", "z\n", "\" id=\"DejaVuSans-4f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 1791 \n", "Q 2906 2416 2648 2759 \n", "Q 2391 3103 1925 3103 \n", "Q 1463 3103 1205 2759 \n", "Q 947 2416 947 1791 \n", "Q 947 1169 1205 825 \n", "Q 1463 481 1925 481 \n", "Q 2391 481 2648 825 \n", "Q 2906 1169 2906 1791 \n", "z\n", "M 3481 434 \n", "Q 3481 -459 3084 -895 \n", "Q 2688 -1331 1869 -1331 \n", "Q 1566 -1331 1297 -1286 \n", "Q 1028 -1241 775 -1147 \n", "L 775 -588 \n", "Q 1028 -725 1275 -790 \n", "Q 1522 -856 1778 -856 \n", "Q 2344 -856 2625 -561 \n", "Q 2906 -266 2906 331 \n", "L 2906 616 \n", "Q 2728 306 2450 153 \n", "Q 2172 0 1784 0 \n", "Q 1141 0 747 490 \n", "Q 353 981 353 1791 \n", "Q 353 2603 747 3093 \n", "Q 1141 3584 1784 3584 \n", "Q 2172 3584 2450 3431 \n", "Q 2728 3278 2906 2969 \n", "L 2906 3500 \n", "L 3481 3500 \n", "L 3481 434 \n", "z\n", "\" id=\"DejaVuSans-67\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 4863 \n", "L 1178 4863 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-6c\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3328 2828 \n", "Q 3544 3216 3844 3400 \n", "Q 4144 3584 4550 3584 \n", "Q 5097 3584 5394 3201 \n", "Q 5691 2819 5691 2113 \n", "L 5691 0 \n", "L 5113 0 \n", "L 5113 2094 \n", "Q 5113 2597 4934 2840 \n", "Q 4756 3084 4391 3084 \n", "Q 3944 3084 3684 2787 \n", "Q 3425 2491 3425 1978 \n", "L 3425 0 \n", "L 2847 0 \n", "L 2847 2094 \n", "Q 2847 2600 2669 2842 \n", "Q 2491 3084 2119 3084 \n", "Q 1678 3084 1418 2786 \n", "Q 1159 2488 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1356 3278 1631 3431 \n", "Q 1906 3584 2284 3584 \n", "Q 2666 3584 2933 3390 \n", "Q 3200 3197 3328 2828 \n", "z\n", "\" id=\"DejaVuSans-6d\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-4f\"/>\n", " <use x=\"78.710938\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"119.824219\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"147.607422\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"211.083984\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"238.867188\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"302.246094\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"363.525391\" xlink:href=\"#DejaVuSans-6c\"/>\n", " <use x=\"391.308594\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"423.095703\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"450.878906\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"548.291016\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"609.570312\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"673.046875\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"174.5\" xlink:href=\"#mbb074bbc39\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- Transformed image -->\n", " <g transform=\"translate(126.21875 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M -19 4666 \n", "L 3928 4666 \n", "L 3928 4134 \n", "L 2272 4134 \n", "L 2272 0 \n", "L 1638 0 \n", "L 1638 4134 \n", "L -19 4134 \n", "L -19 4666 \n", "z\n", "\" id=\"DejaVuSans-54\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2834 3397 \n", "L 2834 2853 \n", "Q 2591 2978 2328 3040 \n", "Q 2066 3103 1784 3103 \n", "Q 1356 3103 1142 2972 \n", "Q 928 2841 928 2578 \n", "Q 928 2378 1081 2264 \n", "Q 1234 2150 1697 2047 \n", "L 1894 2003 \n", "Q 2506 1872 2764 1633 \n", "Q 3022 1394 3022 966 \n", "Q 3022 478 2636 193 \n", "Q 2250 -91 1575 -91 \n", "Q 1294 -91 989 -36 \n", "Q 684 19 347 128 \n", "L 347 722 \n", "Q 666 556 975 473 \n", "Q 1284 391 1588 391 \n", "Q 1994 391 2212 530 \n", "Q 2431 669 2431 922 \n", "Q 2431 1156 2273 1281 \n", "Q 2116 1406 1581 1522 \n", "L 1381 1569 \n", "Q 847 1681 609 1914 \n", "Q 372 2147 372 2553 \n", "Q 372 3047 722 3315 \n", "Q 1072 3584 1716 3584 \n", "Q 2034 3584 2315 3537 \n", "Q 2597 3491 2834 3397 \n", "z\n", "\" id=\"DejaVuSans-73\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2375 4863 \n", "L 2375 4384 \n", "L 1825 4384 \n", "Q 1516 4384 1395 4259 \n", "Q 1275 4134 1275 3809 \n", "L 1275 3500 \n", "L 2222 3500 \n", "L 2222 3053 \n", "L 1275 3053 \n", "L 1275 0 \n", "L 697 0 \n", "L 697 3053 \n", "L 147 3053 \n", "L 147 3500 \n", "L 697 3500 \n", "L 697 3744 \n", "Q 697 4328 969 4595 \n", "Q 1241 4863 1831 4863 \n", "L 2375 4863 \n", "z\n", "\" id=\"DejaVuSans-66\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 2969 \n", "L 2906 4863 \n", "L 3481 4863 \n", "L 3481 0 \n", "L 2906 0 \n", "L 2906 525 \n", "Q 2725 213 2448 61 \n", "Q 2172 -91 1784 -91 \n", "Q 1150 -91 751 415 \n", "Q 353 922 353 1747 \n", "Q 353 2572 751 3078 \n", "Q 1150 3584 1784 3584 \n", "Q 2172 3584 2448 3432 \n", "Q 2725 3281 2906 2969 \n", "z\n", "M 947 1747 \n", "Q 947 1113 1208 752 \n", "Q 1469 391 1925 391 \n", "Q 2381 391 2643 752 \n", "Q 2906 1113 2906 1747 \n", "Q 2906 2381 2643 2742 \n", "Q 2381 3103 1925 3103 \n", "Q 1469 3103 1208 2742 \n", "Q 947 2381 947 1747 \n", "z\n", "\" id=\"DejaVuSans-64\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-54\"/>\n", " <use x=\"46.333984\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"87.447266\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"148.726562\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"212.105469\" xlink:href=\"#DejaVuSans-73\"/>\n", " <use x=\"264.205078\" xlink:href=\"#DejaVuSans-66\"/>\n", " <use x=\"299.410156\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"360.591797\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"399.955078\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"497.367188\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"558.890625\" xlink:href=\"#DejaVuSans-64\"/>\n", " <use x=\"622.367188\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"654.154297\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"681.9375\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"779.349609\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"840.628906\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"904.105469\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 122.4 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 233.9 122.4 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"p32235d7fcf\">\n", " <rect height=\"115.2\" width=\"223.2\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 288x288 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stdout", "output_type": "stream", "text": ["Score original image: 0.03\n", "Score transformed image: -0.00\n"]}], "source": ["img_flipped = exmp_img.flip(dims=(1, 2))\n", "compare_images(exmp_img, img_flipped)"]}, {"cell_type": "markdown", "id": "d6f1c7b3", "metadata": {"papermill": {"duration": 0.036128, "end_time": "2021-09-16T12:40:48.219851", "exception": false, "start_time": "2021-09-16T12:40:48.183723", "status": "completed"}, "tags": []}, "source": ["If the digit can only be read in this way, for example, the 7, then we can see that the score drops.\n", "However, the score only drops slightly.\n", "This is likely because of the small size of our model.\n", "Keep in mind that generative modeling is a much harder task than classification,\n", "as we do not only need to distinguish between classes but learn **all** details/characteristics of the digits.\n", "With a deeper model, this could eventually be captured better (but at the cost of greater training instability).\n", "\n", "Finally, we check what happens if we reduce the digit significantly in size:"]}, {"cell_type": "code", "execution_count": 22, "id": "799ea05d", "metadata": {"execution": {"iopub.execute_input": "2021-09-16T12:40:48.296476Z", "iopub.status.busy": "2021-09-16T12:40:48.296010Z", "iopub.status.idle": "2021-09-16T12:40:48.386691Z", "shell.execute_reply": "2021-09-16T12:40:48.387068Z"}, "papermill": {"duration": 0.131568, "end_time": "2021-09-16T12:40:48.387188", "exception": false, "start_time": "2021-09-16T12:40:48.255620", "status": "completed"}, "tags": []}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["/usr/local/lib/python3.9/dist-packages/torchvision/utils.py:50: UserWarning: range will be deprecated, please use value_range instead.\n", " warnings.warn(warning)\n"]}, {"data": {"application/pdf": "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\n", "image/svg+xml": ["<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<svg height=\"146.278125pt\" version=\"1.1\" viewBox=\"0 0 241.1 146.278125\" width=\"241.1pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-09-16T14:40:48.333827</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " <cc:Agent>\n", " <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n", " </cc:Agent>\n", " </dc:creator>\n", " </cc:Work>\n", " </rdf:RDF>\n", " </metadata>\n", " <defs>\n", " <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n", " </defs>\n", " <g id=\"figure_1\">\n", " <g id=\"patch_1\">\n", " <path d=\"M 0 146.278125 \n", "L 241.1 146.278125 \n", "L 241.1 0 \n", "L 0 0 \n", "z\n", "\" style=\"fill:none;\"/>\n", " </g>\n", " <g id=\"axes_1\">\n", " <g id=\"patch_2\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "L 233.9 7.2 \n", "L 10.7 7.2 \n", "z\n", "\" style=\"fill:#ffffff;\"/>\n", " </g>\n", " <g clip-path=\"url(#pe6c1328a40)\">\n", " <image height=\"116\" id=\"image414c9f03d4\" transform=\"scale(1 -1)translate(0 -116)\" width=\"224\" x=\"10.7\" xlink:href=\"data:image/png;base64,\n", "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\" y=\"-6.4\"/>\n", " </g>\n", " <g id=\"matplotlib.axis_1\">\n", " <g id=\"xtick_1\">\n", " <g id=\"line2d_1\">\n", " <defs>\n", " <path d=\"M 0 0 \n", "L 0 3.5 \n", "\" id=\"m6715979533\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n", " </defs>\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"66.5\" xlink:href=\"#m6715979533\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_1\">\n", " <!-- Original image -->\n", " <g transform=\"translate(29.771094 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M 2522 4238 \n", "Q 1834 4238 1429 3725 \n", "Q 1025 3213 1025 2328 \n", "Q 1025 1447 1429 934 \n", "Q 1834 422 2522 422 \n", "Q 3209 422 3611 934 \n", "Q 4013 1447 4013 2328 \n", "Q 4013 3213 3611 3725 \n", "Q 3209 4238 2522 4238 \n", "z\n", "M 2522 4750 \n", "Q 3503 4750 4090 4092 \n", "Q 4678 3434 4678 2328 \n", "Q 4678 1225 4090 567 \n", "Q 3503 -91 2522 -91 \n", "Q 1538 -91 948 565 \n", "Q 359 1222 359 2328 \n", "Q 359 3434 948 4092 \n", "Q 1538 4750 2522 4750 \n", "z\n", "\" id=\"DejaVuSans-4f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2631 2963 \n", "Q 2534 3019 2420 3045 \n", "Q 2306 3072 2169 3072 \n", "Q 1681 3072 1420 2755 \n", "Q 1159 2438 1159 1844 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1341 3275 1631 3429 \n", "Q 1922 3584 2338 3584 \n", "Q 2397 3584 2469 3576 \n", "Q 2541 3569 2628 3553 \n", "L 2631 2963 \n", "z\n", "\" id=\"DejaVuSans-72\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 3500 \n", "L 1178 3500 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 3500 \n", "z\n", "M 603 4863 \n", "L 1178 4863 \n", "L 1178 4134 \n", "L 603 4134 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-69\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 1791 \n", "Q 2906 2416 2648 2759 \n", "Q 2391 3103 1925 3103 \n", "Q 1463 3103 1205 2759 \n", "Q 947 2416 947 1791 \n", "Q 947 1169 1205 825 \n", "Q 1463 481 1925 481 \n", "Q 2391 481 2648 825 \n", "Q 2906 1169 2906 1791 \n", "z\n", "M 3481 434 \n", "Q 3481 -459 3084 -895 \n", "Q 2688 -1331 1869 -1331 \n", "Q 1566 -1331 1297 -1286 \n", "Q 1028 -1241 775 -1147 \n", "L 775 -588 \n", "Q 1028 -725 1275 -790 \n", "Q 1522 -856 1778 -856 \n", "Q 2344 -856 2625 -561 \n", "Q 2906 -266 2906 331 \n", "L 2906 616 \n", "Q 2728 306 2450 153 \n", "Q 2172 0 1784 0 \n", "Q 1141 0 747 490 \n", "Q 353 981 353 1791 \n", "Q 353 2603 747 3093 \n", "Q 1141 3584 1784 3584 \n", "Q 2172 3584 2450 3431 \n", "Q 2728 3278 2906 2969 \n", "L 2906 3500 \n", "L 3481 3500 \n", "L 3481 434 \n", "z\n", "\" id=\"DejaVuSans-67\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3513 2113 \n", "L 3513 0 \n", "L 2938 0 \n", "L 2938 2094 \n", "Q 2938 2591 2744 2837 \n", "Q 2550 3084 2163 3084 \n", "Q 1697 3084 1428 2787 \n", "Q 1159 2491 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1366 3272 1645 3428 \n", "Q 1925 3584 2291 3584 \n", "Q 2894 3584 3203 3211 \n", "Q 3513 2838 3513 2113 \n", "z\n", "\" id=\"DejaVuSans-6e\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2194 1759 \n", "Q 1497 1759 1228 1600 \n", "Q 959 1441 959 1056 \n", "Q 959 750 1161 570 \n", "Q 1363 391 1709 391 \n", "Q 2188 391 2477 730 \n", "Q 2766 1069 2766 1631 \n", "L 2766 1759 \n", "L 2194 1759 \n", "z\n", "M 3341 1997 \n", "L 3341 0 \n", "L 2766 0 \n", "L 2766 531 \n", "Q 2569 213 2275 61 \n", "Q 1981 -91 1556 -91 \n", "Q 1019 -91 701 211 \n", "Q 384 513 384 1019 \n", "Q 384 1609 779 1909 \n", "Q 1175 2209 1959 2209 \n", "L 2766 2209 \n", "L 2766 2266 \n", "Q 2766 2663 2505 2880 \n", "Q 2244 3097 1772 3097 \n", "Q 1472 3097 1187 3025 \n", "Q 903 2953 641 2809 \n", "L 641 3341 \n", "Q 956 3463 1253 3523 \n", "Q 1550 3584 1831 3584 \n", "Q 2591 3584 2966 3190 \n", "Q 3341 2797 3341 1997 \n", "z\n", "\" id=\"DejaVuSans-61\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 603 4863 \n", "L 1178 4863 \n", "L 1178 0 \n", "L 603 0 \n", "L 603 4863 \n", "z\n", "\" id=\"DejaVuSans-6c\" transform=\"scale(0.015625)\"/>\n", " <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3328 2828 \n", "Q 3544 3216 3844 3400 \n", "Q 4144 3584 4550 3584 \n", "Q 5097 3584 5394 3201 \n", "Q 5691 2819 5691 2113 \n", "L 5691 0 \n", "L 5113 0 \n", "L 5113 2094 \n", "Q 5113 2597 4934 2840 \n", "Q 4756 3084 4391 3084 \n", "Q 3944 3084 3684 2787 \n", "Q 3425 2491 3425 1978 \n", "L 3425 0 \n", "L 2847 0 \n", "L 2847 2094 \n", "Q 2847 2600 2669 2842 \n", "Q 2491 3084 2119 3084 \n", "Q 1678 3084 1418 2786 \n", "Q 1159 2488 1159 1978 \n", "L 1159 0 \n", "L 581 0 \n", "L 581 3500 \n", "L 1159 3500 \n", "L 1159 2956 \n", "Q 1356 3278 1631 3431 \n", "Q 1906 3584 2284 3584 \n", "Q 2666 3584 2933 3390 \n", "Q 3200 3197 3328 2828 \n", "z\n", "\" id=\"DejaVuSans-6d\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 3597 1894 \n", "L 3597 1613 \n", "L 953 1613 \n", "Q 991 1019 1311 708 \n", "Q 1631 397 2203 397 \n", "Q 2534 397 2845 478 \n", "Q 3156 559 3463 722 \n", "L 3463 178 \n", "Q 3153 47 2828 -22 \n", "Q 2503 -91 2169 -91 \n", "Q 1331 -91 842 396 \n", "Q 353 884 353 1716 \n", "Q 353 2575 817 3079 \n", "Q 1281 3584 2069 3584 \n", "Q 2775 3584 3186 3129 \n", "Q 3597 2675 3597 1894 \n", "z\n", "M 3022 2063 \n", "Q 3016 2534 2758 2815 \n", "Q 2500 3097 2075 3097 \n", "Q 1594 3097 1305 2825 \n", "Q 1016 2553 972 2059 \n", "L 3022 2063 \n", "z\n", "\" id=\"DejaVuSans-65\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-4f\"/>\n", " <use x=\"78.710938\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"119.824219\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"147.607422\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"211.083984\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"238.867188\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"302.246094\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"363.525391\" xlink:href=\"#DejaVuSans-6c\"/>\n", " <use x=\"391.308594\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"423.095703\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"450.878906\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"548.291016\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"609.570312\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"673.046875\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"xtick_2\">\n", " <g id=\"line2d_2\">\n", " <g>\n", " <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"174.5\" xlink:href=\"#m6715979533\" y=\"122.4\"/>\n", " </g>\n", " </g>\n", " <g id=\"text_2\">\n", " <!-- Transformed image -->\n", " <g transform=\"translate(126.21875 136.998437)scale(0.1 -0.1)\">\n", " <defs>\n", " <path d=\"M -19 4666 \n", "L 3928 4666 \n", "L 3928 4134 \n", "L 2272 4134 \n", "L 2272 0 \n", "L 1638 0 \n", "L 1638 4134 \n", "L -19 4134 \n", "L -19 4666 \n", "z\n", "\" id=\"DejaVuSans-54\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2834 3397 \n", "L 2834 2853 \n", "Q 2591 2978 2328 3040 \n", "Q 2066 3103 1784 3103 \n", "Q 1356 3103 1142 2972 \n", "Q 928 2841 928 2578 \n", "Q 928 2378 1081 2264 \n", "Q 1234 2150 1697 2047 \n", "L 1894 2003 \n", "Q 2506 1872 2764 1633 \n", "Q 3022 1394 3022 966 \n", "Q 3022 478 2636 193 \n", "Q 2250 -91 1575 -91 \n", "Q 1294 -91 989 -36 \n", "Q 684 19 347 128 \n", "L 347 722 \n", "Q 666 556 975 473 \n", "Q 1284 391 1588 391 \n", "Q 1994 391 2212 530 \n", "Q 2431 669 2431 922 \n", "Q 2431 1156 2273 1281 \n", "Q 2116 1406 1581 1522 \n", "L 1381 1569 \n", "Q 847 1681 609 1914 \n", "Q 372 2147 372 2553 \n", "Q 372 3047 722 3315 \n", "Q 1072 3584 1716 3584 \n", "Q 2034 3584 2315 3537 \n", "Q 2597 3491 2834 3397 \n", "z\n", "\" id=\"DejaVuSans-73\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2375 4863 \n", "L 2375 4384 \n", "L 1825 4384 \n", "Q 1516 4384 1395 4259 \n", "Q 1275 4134 1275 3809 \n", "L 1275 3500 \n", "L 2222 3500 \n", "L 2222 3053 \n", "L 1275 3053 \n", "L 1275 0 \n", "L 697 0 \n", "L 697 3053 \n", "L 147 3053 \n", "L 147 3500 \n", "L 697 3500 \n", "L 697 3744 \n", "Q 697 4328 969 4595 \n", "Q 1241 4863 1831 4863 \n", "L 2375 4863 \n", "z\n", "\" id=\"DejaVuSans-66\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 1959 3097 \n", "Q 1497 3097 1228 2736 \n", "Q 959 2375 959 1747 \n", "Q 959 1119 1226 758 \n", "Q 1494 397 1959 397 \n", "Q 2419 397 2687 759 \n", "Q 2956 1122 2956 1747 \n", "Q 2956 2369 2687 2733 \n", "Q 2419 3097 1959 3097 \n", "z\n", "M 1959 3584 \n", "Q 2709 3584 3137 3096 \n", "Q 3566 2609 3566 1747 \n", "Q 3566 888 3137 398 \n", "Q 2709 -91 1959 -91 \n", "Q 1206 -91 779 398 \n", "Q 353 888 353 1747 \n", "Q 353 2609 779 3096 \n", "Q 1206 3584 1959 3584 \n", "z\n", "\" id=\"DejaVuSans-6f\" transform=\"scale(0.015625)\"/>\n", " <path d=\"M 2906 2969 \n", "L 2906 4863 \n", "L 3481 4863 \n", "L 3481 0 \n", "L 2906 0 \n", "L 2906 525 \n", "Q 2725 213 2448 61 \n", "Q 2172 -91 1784 -91 \n", "Q 1150 -91 751 415 \n", "Q 353 922 353 1747 \n", "Q 353 2572 751 3078 \n", "Q 1150 3584 1784 3584 \n", "Q 2172 3584 2448 3432 \n", "Q 2725 3281 2906 2969 \n", "z\n", "M 947 1747 \n", "Q 947 1113 1208 752 \n", "Q 1469 391 1925 391 \n", "Q 2381 391 2643 752 \n", "Q 2906 1113 2906 1747 \n", "Q 2906 2381 2643 2742 \n", "Q 2381 3103 1925 3103 \n", "Q 1469 3103 1208 2742 \n", "Q 947 2381 947 1747 \n", "z\n", "\" id=\"DejaVuSans-64\" transform=\"scale(0.015625)\"/>\n", " </defs>\n", " <use xlink:href=\"#DejaVuSans-54\"/>\n", " <use x=\"46.333984\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"87.447266\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"148.726562\" xlink:href=\"#DejaVuSans-6e\"/>\n", " <use x=\"212.105469\" xlink:href=\"#DejaVuSans-73\"/>\n", " <use x=\"264.205078\" xlink:href=\"#DejaVuSans-66\"/>\n", " <use x=\"299.410156\" xlink:href=\"#DejaVuSans-6f\"/>\n", " <use x=\"360.591797\" xlink:href=\"#DejaVuSans-72\"/>\n", " <use x=\"399.955078\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"497.367188\" xlink:href=\"#DejaVuSans-65\"/>\n", " <use x=\"558.890625\" xlink:href=\"#DejaVuSans-64\"/>\n", " <use x=\"622.367188\" xlink:href=\"#DejaVuSans-20\"/>\n", " <use x=\"654.154297\" xlink:href=\"#DejaVuSans-69\"/>\n", " <use x=\"681.9375\" xlink:href=\"#DejaVuSans-6d\"/>\n", " <use x=\"779.349609\" xlink:href=\"#DejaVuSans-61\"/>\n", " <use x=\"840.628906\" xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"904.105469\" xlink:href=\"#DejaVuSans-65\"/>\n", " </g>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"matplotlib.axis_2\"/>\n", " <g id=\"patch_3\">\n", " <path d=\"M 10.7 122.4 \n", "L 10.7 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_4\">\n", " <path d=\"M 233.9 122.4 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_5\">\n", " <path d=\"M 10.7 122.4 \n", "L 233.9 122.4 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " <g id=\"patch_6\">\n", " <path d=\"M 10.7 7.2 \n", "L 233.9 7.2 \n", "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <defs>\n", " <clipPath id=\"pe6c1328a40\">\n", " <rect height=\"115.2\" width=\"223.2\" x=\"10.7\" y=\"7.2\"/>\n", " </clipPath>\n", " </defs>\n", "</svg>\n"], "text/plain": ["<Figure size 288x288 with 1 Axes>"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}, {"name": "stdout", "output_type": "stream", "text": ["Score original image: 0.03\n", "Score transformed image: -0.02\n"]}], "source": ["img_tiny = torch.zeros_like(exmp_img) - 1\n", "img_tiny[:, exmp_img.shape[1] // 2 :, exmp_img.shape[2] // 2 :] = exmp_img[:, ::2, ::2]\n", "compare_images(exmp_img, img_tiny)"]}, {"cell_type": "markdown", "id": "abbe7583", "metadata": {"papermill": {"duration": 0.037748, "end_time": "2021-09-16T12:40:48.462802", "exception": false, "start_time": "2021-09-16T12:40:48.425054", "status": "completed"}, "tags": []}, "source": ["The score again drops but not by a large margin, although digits in the MNIST dataset usually are much larger.\n", "\n", "Overall, we can conclude that our model is good for detecting Gaussian noise and smaller transformations to existing digits.\n", "Nonetheless, to obtain a very good out-of-distribution model, we would need to train deeper models and for more iterations."]}, {"cell_type": "markdown", "id": "714313c8", "metadata": {"papermill": {"duration": 0.037582, "end_time": "2021-09-16T12:40:48.538109", "exception": false, "start_time": "2021-09-16T12:40:48.500527", "status": "completed"}, "tags": []}, "source": ["### Instability\n", "\n", "Finally, we should discuss the possible instabilities of energy-based models,\n", "in particular for the example of image generation that we have implemented in this notebook.\n", "In the process of hyperparameter search for this notebook, there have been several models that diverged.\n", "Divergence in energy-based models means that the models assign a high probability to examples of the training set which is a good thing.\n", "However, at the same time, the sampling algorithm fails and only generates noise images that obtain minimal probability scores.\n", "This happens because the model has created many local maxima in which the generated noise images fall.\n", "The energy surface over which we calculate the gradients to reach data points with high probability has \"diverged\" and is not useful for our MCMC sampling.\n", "\n", "Besides finding the optimal hyperparameters, a common trick in energy-based models is to reload stable checkpoints.\n", "If we detect that the model is diverging, we stop the training, load the model from one epoch ago where it did not diverge yet.\n", "Afterward, we continue training and hope that with a different seed the model is not diverging again.\n", "Nevertheless, this should be considered as the \"last hope\" for stabilizing the models,\n", "and careful hyperparameter tuning is the better way to do so.\n", "Sensitive hyperparameters include `step_size`, `steps` and the noise standard deviation in the sampler,\n", "and the learning rate and feature dimensionality in the CNN model."]}, {"cell_type": "markdown", "id": "a34043a7", "metadata": {"papermill": {"duration": 0.037416, "end_time": "2021-09-16T12:40:48.621320", "exception": false, "start_time": "2021-09-16T12:40:48.583904", "status": "completed"}, "tags": []}, "source": ["## Conclusion\n", "\n", "In this tutorial, we have discussed energy-based models for generative modeling.\n", "The concept relies on the idea that any strictly positive function can be turned into a probability\n", "distribution by normalizing over the whole dataset.\n", "As this is not reasonable to calculate for high dimensional data like images,\n", "we train the model using contrastive divergence and sampling via MCMC.\n", "While the idea allows us to turn any neural network into an energy-based model,\n", "we have seen that there are multiple training tricks needed to stabilize the training.\n", "Furthermore, the training time of these models is relatively long as, during every training iteration,\n", "we need to sample new \"fake\" images, even with a sampling buffer.\n", "In the next lectures and assignment, we will see different generative models (e.g. VAE, GAN, NF)\n", "that allow us to do generative modeling more stably, but with the cost of more parameters."]}, {"cell_type": "markdown", "id": "6ca06d61", "metadata": {"papermill": {"duration": 0.038052, "end_time": "2021-09-16T12:40:48.697258", "exception": false, "start_time": "2021-09-16T12:40:48.659206", "status": "completed"}, "tags": []}, "source": ["## Congratulations - Time to Join the Community!\n", "\n", "Congratulations on completing this notebook tutorial! If you enjoyed this and would like to join the Lightning\n", "movement, you can do so in the following ways!\n", "\n", "### Star [Lightning](https://github.com/PyTorchLightning/pytorch-lightning) on GitHub\n", "The easiest way to help our community is just by starring the GitHub repos! This helps raise awareness of the cool\n", "tools we're building.\n", "\n", "### Join our [Slack](https://join.slack.com/t/pytorch-lightning/shared_invite/zt-pw5v393p-qRaDgEk24~EjiZNBpSQFgQ)!\n", "The best way to keep up to date on the latest advancements is to join our community! Make sure to introduce yourself\n", "and share your interests in `#general` channel\n", "\n", "\n", "### Contributions !\n", "The best way to contribute to our community is to become a code contributor! At any time you can go to\n", "[Lightning](https://github.com/PyTorchLightning/pytorch-lightning) or [Bolt](https://github.com/PyTorchLightning/lightning-bolts)\n", "GitHub Issues page and filter for \"good first issue\".\n", "\n", "* [Lightning good first issue](https://github.com/PyTorchLightning/pytorch-lightning/issues?q=is%3Aopen+is%3Aissue+label%3A%22good+first+issue%22)\n", "* [Bolt good first issue](https://github.com/PyTorchLightning/lightning-bolts/issues?q=is%3Aopen+is%3Aissue+label%3A%22good+first+issue%22)\n", "* You can also contribute your own notebooks with useful examples !\n", "\n", "### Great thanks from the entire Pytorch Lightning Team for your interest !\n", "\n", "{height=\"60px\" width=\"240px\"}"]}, {"cell_type": "raw", "metadata": {"raw_mimetype": "text/restructuredtext"}, "source": [".. customcarditem::\n", " :header: Tutorial 7: Deep Energy-Based Generative Models\n", " :card_description: In this tutorial, we will look at energy-based deep learning models, and focus on their application as generative models. Energy models have been a popular tool before the...\n", " :tags: Image,GPU/TPU,UvA-DL-Course\n", " :image: _static/images/course_UvA-DL/07-deep-energy-based-generative-models.jpg"]}], "metadata": {"jupytext": {"cell_metadata_filter": "colab_type,id,colab,-all", "formats": "ipynb,py:percent", "main_language": "python"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7"}, "papermill": {"default_parameters": {}, "duration": 11.264697, "end_time": "2021-09-16T12:40:49.242921", "environment_variables": {}, "exception": null, "input_path": "course_UvA-DL/07-deep-energy-based-generative-models/Deep_Energy_Models.ipynb", "output_path": ".notebooks/course_UvA-DL/07-deep-energy-based-generative-models.ipynb", "parameters": {}, "start_time": "2021-09-16T12:40:37.978224", "version": "2.3.3"}}, "nbformat": 4, "nbformat_minor": 5}