---
title: Cosine Similarity
description: Compute the Cosine Similarity.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/regression/cosine_similarity'
---
# Cosine Similarity {#cosine-similarity}

## Module Interface {#module-interface}

### `class torchmetrics.CosineSimilarity(reduction='sum', **kwargs)` {#torchmetrics.CosineSimilarity}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/cosine_similarity.py#L30-L139)

Compute the [Cosine Similarity](https://en.wikipedia.org/wiki/Cosine_similarity).

```math
cos_{sim}(x,y) = \frac{x \cdot y}{||x|| \cdot ||y||} = \frac{\sum_{i=1}^n x_i y_i}{\sqrt{\sum_{i=1}^n x_i^2}\sqrt{\sum_{i=1}^n y_i^2}}
```

where $`y`$ is a tensor of target values, and $`x`$ is a tensor of predictions.

As input to `forward` and `update` the metric accepts the following input:

*   `preds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Predicted float tensor with shape `(N,d)`
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Ground truth float tensor with shape `(N,d)`
    

As output of `forward` and `compute` the metric returns the following output:

*   `cosine_similarity` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A float tensor with the cosine similarity
    

Parameters:

*   **reduction** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'mean'`, `'sum'`, `'none'`, `None`\]) – how to reduce over the batch dimension using ‘sum’, ‘mean’ or ‘none’ (taking the individual scores)
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example

```python
>>> from torch import tensor
>>> from torchmetrics.regression import CosineSimilarity
>>> target = tensor([[0, 1], [1, 1]])
>>> preds = tensor([[0, 1], [0, 1]])
>>> cosine_similarity = CosineSimilarity(reduction = 'mean')
>>> cosine_similarity(preds, target)
tensor(0.8536)
```

#### `plot(val=None, ax=None)` {#torchmetrics.CosineSimilarity.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/cosine_similarity.py#L99-L139)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import CosineSimilarity
>>> metric = CosineSimilarity()
>>> metric.update(randn(10,2), randn(10,2))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/cosine\_similarity-1.png](/docs/torchmetrics/1.9.0/static/_images/cosine_similarity-1.png)](/docs/torchmetrics/1.9.0/static/_images/cosine_similarity-1.png)

```python
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import CosineSimilarity
>>> metric = CosineSimilarity()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,2), randn(10,2)))
>>> fig, ax = metric.plot(values)
```

[![../../\_images/cosine\_similarity-2.png](/docs/torchmetrics/1.9.0/static/_images/cosine_similarity-2.png)](/docs/torchmetrics/1.9.0/static/_images/cosine_similarity-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.cosine_similarity(preds, target, reduction='sum')` {#torchmetrics.functional.cosine_similarity}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/regression/cosine_similarity.py#L75-L101)

Compute the [Cosine Similarity](https://en.wikipedia.org/wiki/Cosine_similarity).

```math
cos_{sim}(x,y) = \frac{x \cdot y}{||x|| \cdot ||y||} = \frac{\sum_{i=1}^n x_i y_i}{\sqrt{\sum_{i=1}^n x_i^2}\sqrt{\sum_{i=1}^n y_i^2}}
```

where $`y`$ is a tensor of target values, and $`x`$ is a tensor of predictions.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Predicted tensor with shape `(N,d)`
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Ground truth tensor with shape `(N,d)`
    
*   **reduction** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`str`](https://docs.python.org/3/builtins/stdtypes.html#str "(in Python v3.15)")\]) – The method of reducing along the batch dimension using sum, mean or taking the individual scores
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

Example

```python
>>> from torchmetrics.functional.regression import cosine_similarity
>>> target = torch.tensor([[1, 2, 3, 4],
...                        [1, 2, 3, 4]])
>>> preds = torch.tensor([[1, 2, 3, 4],
...                       [-1, -2, -3, -4]])
>>> cosine_similarity(preds, target, 'none')
tensor([ 1.0000, -1.0000])
```

---

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- Parent: [Regression](/docs/torchmetrics/1.9.0/regression.md)