---
title: Hamming Distance
description: Compute the average Hamming distance (also known as Hamming loss).
canonical: 'https://lightning.ai/docs/torchmetrics/stable/classification/hamming_distance'
---
# Hamming Distance {#hamming-distance}

## Module Interface {#module-interface}

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L469-L529)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss).

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the `task` argument to either `'binary'`, `'multiclass'` or `'multilabel'`. See the documentation of [`BinaryHammingDistance`](#torchmetrics.classification.BinaryHammingDistance "torchmetrics.classification.BinaryHammingDistance"), [`MulticlassHammingDistance`](#torchmetrics.classification.MulticlassHammingDistance "torchmetrics.classification.MulticlassHammingDistance") and [`MultilabelHammingDistance`](#torchmetrics.classification.MultilabelHammingDistance "torchmetrics.classification.MultilabelHammingDistance") for the specific details of each argument influence and examples.

Legacy Example:

```python
>>> from torch import tensor
>>> target = tensor([[0, 1], [1, 1]])
>>> preds = tensor([[0, 1], [0, 1]])
>>> hamming_distance = HammingDistance(task="multilabel", num_labels=2)
>>> hamming_distance(preds, target)
tensor(0.2500)
```

#### `static __new__(cls, task, threshold=0.5, num_classes=None, num_labels=None, average='micro', multidim_average='global', top_k=1, ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.HammingDistance.__new__}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L496-L529)

Initialize task metric.

Return type:

[`Metric`](/docs/torchmetrics/1.9.0/api-reference/metric.md#torchmetrics.Metric "torchmetrics.metric.Metric")

### BinaryHammingDistance {#binaryhammingdistance}

### `class torchmetrics.classification.BinaryHammingDistance(threshold=0.5, multidim_average='global', ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.BinaryHammingDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L36-L158)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for binary tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

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)")): An int or float tensor of shape `(N, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): An int tensor of shape `(N, ...)`.
    

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

*   `bhd` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor whose returned shape depends on the `multidim_average` arguments:
    
    *   If `multidim_average` is set to `global`, the metric returns a scalar value.
        
    *   If `multidim_average` is set to `samplewise`, the metric returns `(N,)` vector consisting of a scalar value per sample.
        

If `multidim_average` is set to `samplewise` we expect at least one additional dimension `...` to be present, which the reduction will then be applied over instead of the sample dimension `N`.

Parameters:

*   **threshold** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Threshold for transforming probability to binary {0,1} predictions
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = tensor([0, 1, 0, 1, 0, 1])
>>> preds = tensor([0, 0, 1, 1, 0, 1])
>>> metric = BinaryHammingDistance()
>>> metric(preds, target)
tensor(0.3333)
```

Example (preds is float tensor):

```python
>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = tensor([0, 1, 0, 1, 0, 1])
>>> preds = tensor([0.11, 0.22, 0.84, 0.73, 0.33, 0.92])
>>> metric = BinaryHammingDistance()
>>> metric(preds, target)
tensor(0.3333)
```

Example (multidim tensors):

```python
>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = tensor([[[0.59, 0.91], [0.91, 0.99],  [0.63, 0.04]],
...                 [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]]])
>>> metric = BinaryHammingDistance(multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.6667, 0.8333])
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L118-L158)

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 object and Axes object

Raises:

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

```python
>>> # Example plotting a single value
>>> from torch import rand, randint
>>> from torchmetrics.classification import BinaryHammingDistance
>>> metric = BinaryHammingDistance()
>>> metric.update(rand(10), randint(2,(10,)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/hamming\_distance-1.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-1.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-1.png)

```python
>>> # Example plotting multiple values
>>> from torch import rand, randint
>>> from torchmetrics.classification import BinaryHammingDistance
>>> metric = BinaryHammingDistance()
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(rand(10), randint(2,(10,))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/hamming\_distance-2.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-2.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-2.png)

### MulticlassHammingDistance {#multiclasshammingdistance}

### `class torchmetrics.classification.MulticlassHammingDistance(num_classes=None, top_k=1, average='macro', multidim_average='global', ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.MulticlassHammingDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L161-L312)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for multiclass tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

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)")): An int tensor of shape `(N, ...)` or float tensor of shape `(N, C, ..)`. If preds is a floating point we apply `torch.argmax` along the `C` dimension to automatically convert probabilities/logits into an int tensor.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): An int tensor of shape `(N, ...)`.
    

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

*   `mchd` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor whose returned shape depends on the `average` and `multidim_average` arguments:
    
    *   If `multidim_average` is set to `global`:
        
        *   If `average='micro'/'macro'/'weighted'`, the output will be a scalar tensor
            
        *   If `average=None/'none'`, the shape will be `(C,)`
            
    *   If `multidim_average` is set to `samplewise`:
        
        *   If `average='micro'/'macro'/'weighted'`, the shape will be `(N,)`
            
        *   If `average=None/'none'`, the shape will be `(N, C)`
            

If `multidim_average` is set to `samplewise` we expect at least one additional dimension `...` to be present, which the reduction will then be applied over instead of the sample dimension `N`.

Parameters:

*   **num\_classes** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Integer specifying the number of classes
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **top\_k** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of highest probability or logit score predictions considered to find the correct label. Only works when `preds` contain probabilities/logits.
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([2, 1, 0, 1])
>>> metric = MulticlassHammingDistance(num_classes=3)
>>> metric(preds, target)
tensor(0.1667)
>>> mchd = MulticlassHammingDistance(num_classes=3, average=None)
>>> mchd(preds, target)
tensor([0.5000, 0.0000, 0.0000])
```

Example (preds is float tensor):

```python
>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([[0.16, 0.26, 0.58],
...                 [0.22, 0.61, 0.17],
...                 [0.71, 0.09, 0.20],
...                 [0.05, 0.82, 0.13]])
>>> metric = MulticlassHammingDistance(num_classes=3)
>>> metric(preds, target)
tensor(0.1667)
>>> mchd = MulticlassHammingDistance(num_classes=3, average=None)
>>> mchd(preds, target)
tensor([0.5000, 0.0000, 0.0000])
```

Example (multidim tensors):

```python
>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = tensor([[[0, 1], [2, 1], [0, 2]], [[1, 1], [2, 0], [1, 2]]])
>>> preds = tensor([[[0, 2], [2, 0], [0, 1]], [[2, 2], [2, 1], [1, 0]]])
>>> metric = MulticlassHammingDistance(num_classes=3, multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.5000, 0.7222])
>>> mchd = MulticlassHammingDistance(num_classes=3, multidim_average='samplewise', average=None)
>>> mchd(preds, target)
tensor([[0.0000, 1.0000, 0.5000],
        [1.0000, 0.6667, 0.5000]])
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L272-L312)

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 object and Axes object

Raises:

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

```python
>>> # Example plotting a single value per class
>>> from torch import randint
>>> from torchmetrics.classification import MulticlassHammingDistance
>>> metric = MulticlassHammingDistance(num_classes=3, average=None)
>>> metric.update(randint(3, (20,)), randint(3, (20,)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/hamming\_distance-3.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-3.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-3.png)

```python
>>> # Example plotting a multiple values per class
>>> from torch import randint
>>> from torchmetrics.classification import MulticlassHammingDistance
>>> metric = MulticlassHammingDistance(num_classes=3, average=None)
>>> values = []
>>> for _ in range(20):
...     values.append(metric(randint(3, (20,)), randint(3, (20,))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/hamming\_distance-4.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-4.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-4.png)

### MultilabelHammingDistance {#multilabelhammingdistance}

### `class torchmetrics.classification.MultilabelHammingDistance(num_labels, threshold=0.5, average='macro', multidim_average='global', ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.MultilabelHammingDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L315-L466)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for multilabel tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

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)")): An int tensor or float tensor of shape `(N, C, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): An int tensor of shape `(N, C, ...)`.
    

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

*   `mlhd` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor whose returned shape depends on the `average` and `multidim_average` arguments:
    
    *   If `multidim_average` is set to `global`:
        
        *   If `average='micro'/'macro'/'weighted'`, the output will be a scalar tensor
            
        *   If `average=None/'none'`, the shape will be `(C,)`
            
    *   If `multidim_average` is set to `samplewise`:
        
        *   If `average='micro'/'macro'/'weighted'`, the shape will be `(N,)`
            
        *   If `average=None/'none'`, the shape will be `(N, C)`
            

If `multidim_average` is set to `samplewise` we expect at least one additional dimension `...` to be present, which the reduction will then be applied over instead of the sample dimension `N`.

Parameters:

*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **threshold** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0, 0, 1], [1, 0, 1]])
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)
>>> mlhd = MultilabelHammingDistance(num_labels=3, average=None)
>>> mlhd(preds, target)
tensor([0.0000, 0.5000, 0.5000])
```

Example (preds is float tensor):

```python
>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)
>>> mlhd = MultilabelHammingDistance(num_labels=3, average=None)
>>> mlhd(preds, target)
tensor([0.0000, 0.5000, 0.5000])
```

Example (multidim tensors):

```python
>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = tensor([[[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...                 [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]]])
>>> metric = MultilabelHammingDistance(num_labels=3, multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.6667, 0.8333])
>>> mlhd = MultilabelHammingDistance(num_labels=3, multidim_average='samplewise', average=None)
>>> mlhd(preds, target)
tensor([[0.5000, 0.5000, 1.0000],
        [1.0000, 1.0000, 0.5000]])
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/hamming.py#L426-L466)

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
>>> # Example plotting a single value
>>> from torch import rand, randint
>>> from torchmetrics.classification import MultilabelHammingDistance
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> metric.update(randint(2, (20, 3)), randint(2, (20, 3)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/hamming\_distance-5.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-5.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-5.png)

```python
>>> # Example plotting multiple values
>>> from torch import rand, randint
>>> from torchmetrics.classification import MultilabelHammingDistance
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(randint(2, (20, 3)), randint(2, (20, 3))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/hamming\_distance-6.png](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-6.png)](/docs/torchmetrics/1.9.0/static/_images/hamming_distance-6.png)

## Functional Interface {#functional-interface}

### hamming_distance {#hamming-distance}

### `torchmetrics.functional.hamming_distance(preds, target, task, threshold=0.5, num_classes=None, num_labels=None, average='micro', multidim_average='global', top_k=1, ignore_index=None, validate_args=True)` {#torchmetrics.functional.hamming_distance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/hamming.py#L374-L429)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss). :rtype: [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the `task` argument to either `'binary'`, `'multiclass'` or `'multilabel'`. See the documentation of [`binary_hamming_distance()`](#torchmetrics.functional.classification.binary_hamming_distance "torchmetrics.functional.classification.binary_hamming_distance"), [`multiclass_hamming_distance()`](#torchmetrics.functional.classification.multiclass_hamming_distance "torchmetrics.functional.classification.multiclass_hamming_distance") and [`multilabel_hamming_distance()`](#torchmetrics.functional.classification.multilabel_hamming_distance "torchmetrics.functional.classification.multilabel_hamming_distance") for the specific details of each argument influence and examples.

Legacy Example:

```python
>>> from torch import tensor
>>> target = tensor([[0, 1], [1, 1]])
>>> preds = tensor([[0, 1], [0, 1]])
>>> hamming_distance(preds, target, task="binary")
tensor(0.2500)
```

### binary_hamming_distance {#binary-hamming-distance}

### `torchmetrics.functional.classification.binary_hamming_distance(preds, target, threshold=0.5, multidim_average='global', ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.binary_hamming_distance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/hamming.py#L86-L159)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for binary tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

Accepts the following input tensors:

*   `preds` (int or float tensor): `(N, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` (int tensor): `(N, ...)`
    

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **threshold** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Threshold for transforming probability to binary {0,1} predictions
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Return type:

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

Returns:

If `multidim_average` is set to `global`, the metric returns a scalar value. If `multidim_average` is set to `samplewise`, the metric returns `(N,)` vector consisting of a scalar value per sample.

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = tensor([0, 1, 0, 1, 0, 1])
>>> preds = tensor([0, 0, 1, 1, 0, 1])
>>> binary_hamming_distance(preds, target)
tensor(0.3333)
```

Example (preds is float tensor):

```python
>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = tensor([0, 1, 0, 1, 0, 1])
>>> preds = tensor([0.11, 0.22, 0.84, 0.73, 0.33, 0.92])
>>> binary_hamming_distance(preds, target)
tensor(0.3333)
```

Example (multidim tensors):

```python
>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = tensor([[[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...                 [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]]])
>>> binary_hamming_distance(preds, target, multidim_average='samplewise')
tensor([0.6667, 0.8333])
```

### multiclass_hamming_distance {#multiclass-hamming-distance}

### `torchmetrics.functional.classification.multiclass_hamming_distance(preds, target, num_classes, average='macro', top_k=1, multidim_average='global', ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.multiclass_hamming_distance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/hamming.py#L162-L268)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for multiclass tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

Accepts the following input tensors:

*   `preds`: `(N, ...)` (int tensor) or `(N, C, ..)` (float tensor). If preds is a floating point we apply `torch.argmax` along the `C` dimension to automatically convert probabilities/logits into an int tensor.
    
*   `target` (int tensor): `(N, ...)`
    

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **num\_classes** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of classes
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **top\_k** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of highest probability or logit score predictions considered to find the correct label. Only works when `preds` contain probabilities/logits.
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Returns:

*   If `multidim_average` is set to `global`:
    
    *   If `average='micro'/'macro'/'weighted'`, the output will be a scalar tensor
        
    *   If `average=None/'none'`, the shape will be `(C,)`
        
*   If `multidim_average` is set to `samplewise`:
    
    *   If `average='micro'/'macro'/'weighted'`, the shape will be `(N,)`
        
    *   If `average=None/'none'`, the shape will be `(N, C)`
        

Return type:

The returned shape depends on the `average` and `multidim_average` arguments

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([2, 1, 0, 1])
>>> multiclass_hamming_distance(preds, target, num_classes=3)
tensor(0.1667)
>>> multiclass_hamming_distance(preds, target, num_classes=3, average=None)
tensor([0.5000, 0.0000, 0.0000])
```

Example (preds is float tensor):

```python
>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([[0.16, 0.26, 0.58],
...                 [0.22, 0.61, 0.17],
...                 [0.71, 0.09, 0.20],
...                 [0.05, 0.82, 0.13]])
>>> multiclass_hamming_distance(preds, target, num_classes=3)
tensor(0.1667)
>>> multiclass_hamming_distance(preds, target, num_classes=3, average=None)
tensor([0.5000, 0.0000, 0.0000])
```

Example (multidim tensors):

```python
>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = tensor([[[0, 1], [2, 1], [0, 2]], [[1, 1], [2, 0], [1, 2]]])
>>> preds = tensor([[[0, 2], [2, 0], [0, 1]], [[2, 2], [2, 1], [1, 0]]])
>>> multiclass_hamming_distance(preds, target, num_classes=3, multidim_average='samplewise')
tensor([0.5000, 0.7222])
>>> multiclass_hamming_distance(preds, target, num_classes=3, multidim_average='samplewise', average=None)
tensor([[0.0000, 1.0000, 0.5000],
        [1.0000, 0.6667, 0.5000]])
```

### multilabel_hamming_distance {#multilabel-hamming-distance}

### `torchmetrics.functional.classification.multilabel_hamming_distance(preds, target, num_labels, threshold=0.5, average='macro', multidim_average='global', ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.multilabel_hamming_distance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/hamming.py#L271-L371)

Compute the average [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance) (also known as Hamming loss) for multilabel tasks.

```math
\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})
```

Where $`y`$ is a tensor of target values, $`\hat{y}`$ is a tensor of predictions, and $`\bullet_{il}`$ refers to the $`l`$\-th label of the $`i`$\-th sample of that tensor.

Accepts the following input tensors:

*   `preds` (int or float tensor): `(N, C, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` (int tensor): `(N, C, ...)`
    

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **threshold** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **multidim\_average** ([`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'global'`, `'samplewise'`\]) –
    
    Defines how additionally dimensions `...` should be handled. Should be one of the following:
    
    *   `global`: Additional dimensions are flatted along the batch dimension
        
    *   `samplewise`: Statistic will be calculated independently for each sample on the `N` axis. The statistics in this case are calculated over the additional dimensions.
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Returns:

*   If `multidim_average` is set to `global`:
    
    *   If `average='micro'/'macro'/'weighted'`, the output will be a scalar tensor
        
    *   If `average=None/'none'`, the shape will be `(C,)`
        
*   If `multidim_average` is set to `samplewise`:
    
    *   If `average='micro'/'macro'/'weighted'`, the shape will be `(N,)`
        
    *   If `average=None/'none'`, the shape will be `(N, C)`
        

Return type:

The returned shape depends on the `average` and `multidim_average` arguments

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0, 0, 1], [1, 0, 1]])
>>> multilabel_hamming_distance(preds, target, num_labels=3)
tensor(0.3333)
>>> multilabel_hamming_distance(preds, target, num_labels=3, average=None)
tensor([0.0000, 0.5000, 0.5000])
```

Example (preds is float tensor):

```python
>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> multilabel_hamming_distance(preds, target, num_labels=3)
tensor(0.3333)
>>> multilabel_hamming_distance(preds, target, num_labels=3, average=None)
tensor([0.0000, 0.5000, 0.5000])
```

Example (multidim tensors):

```python
>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = tensor([[[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...                 [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]]])
>>> multilabel_hamming_distance(preds, target, num_labels=3, multidim_average='samplewise')
tensor([0.6667, 0.8333])
>>> multilabel_hamming_distance(preds, target, num_labels=3, multidim_average='samplewise', average=None)
tensor([[0.5000, 0.5000, 1.0000],
        [1.0000, 1.0000, 0.5000]])
```

---

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