---
title: Mean Squared Log Error (MSLE)
description: Compute mean squared logarithmic error (MSLE).
canonical: >-
  https://lightning.ai/docs/torchmetrics/stable/regression/mean_squared_log_error
---
# Mean Squared Log Error (MSLE) {#mean-squared-log-error-msle}

## Module Interface {#module-interface}

### `class torchmetrics.MeanSquaredLogError(**kwargs)` {#torchmetrics.MeanSquaredLogError}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/log_mse.py#L28-L129)

Compute [mean squared logarithmic error](https://scikit-learn.org/stable/modules/model_evaluation.html#mean-squared-log-error) (MSLE).

```math
\text{MSLE} = \frac{1}{N}\sum_i^N (\log_e(1 + y_i) - \log_e(1 + \hat{y_i}))^2
```

Where $`y`$ is a tensor of target values, and $`\hat{y}`$ 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)")): Predictions from model
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Ground truth values
    

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

*   `mean_squared_log_error` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor with the mean squared log error
    

Parameters:

**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 MeanSquaredLogError
>>> target = tensor([2.5, 5, 4, 8])
>>> preds = tensor([3, 5, 2.5, 7])
>>> mean_squared_log_error = MeanSquaredLogError()
>>> mean_squared_log_error(preds, target)
tensor(0.0397)
```

Attention

Half precision is only support on GPU for this metric.

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/log_mse.py#L89-L129)

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 MeanSquaredLogError
>>> metric = MeanSquaredLogError()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/mean\_squared\_log\_error-1.png](/docs/torchmetrics/1.9.0/static/_images/mean_squared_log_error-1.png)](/docs/torchmetrics/1.9.0/static/_images/mean_squared_log_error-1.png)

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

[![../../\_images/mean\_squared\_log\_error-2.png](/docs/torchmetrics/1.9.0/static/_images/mean_squared_log_error-2.png)](/docs/torchmetrics/1.9.0/static/_images/mean_squared_log_error-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.mean_squared_log_error(preds, target)` {#torchmetrics.functional.mean_squared_log_error}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/regression/log_mse.py#L54-L76)

Compute mean squared log error.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – estimated labels
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – ground truth labels
    

Return type:

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

Returns:

Tensor with RMSLE

Example

```python
>>> from torchmetrics.functional.regression import mean_squared_log_error
>>> x = torch.tensor([0., 1, 2, 3])
>>> y = torch.tensor([0., 1, 2, 2])
>>> mean_squared_log_error(x, y)
tensor(0.0207)
```

Attention

Half precision is only support on GPU for this metric.

---

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