# torch.nn.functional¶

## Convolution functions¶

### conv1d¶

torch.nn.functional.conv1d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 1D convolution over an input signal composed of several input planes.

See Conv1d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iW)$

• weight – filters of shape $(\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kW)$

• bias – optional bias of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a one-element tuple (sW,). Default: 1

• padding – implicit paddings on both sides of the input. Can be a single number or a one-element tuple (padW,). Default: 0

• dilation – the spacing between kernel elements. Can be a single number or a one-element tuple (dW,). Default: 1

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3)
>>> inputs = torch.randn(20, 16, 50)
>>> F.conv1d(inputs, filters)


### conv2d¶

torch.nn.functional.conv2d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 2D convolution over an input image composed of several input planes.

See Conv2d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iH , iW)$

• weight – filters of shape $(\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kH , kW)$

• bias – optional bias tensor of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1

• padding – implicit paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0

• dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

Examples:

>>> # With square kernels and equal stride
>>> filters = torch.randn(8,4,3,3)
>>> inputs = torch.randn(1,4,5,5)


### conv3d¶

torch.nn.functional.conv3d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 3D convolution over an input image composed of several input planes.

See Conv3d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iT , iH , iW)$

• weight – filters of shape $(\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kT , kH , kW)$

• bias – optional bias tensor of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1

• dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3, 3, 3)
>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> F.conv3d(inputs, filters)


### conv_transpose1d¶

torch.nn.functional.conv_transpose1d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 1D transposed convolution operator over an input signal composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose1d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iW)$

• weight – filters of shape $(\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kW)$

• bias – optional bias of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a tuple (sW,). Default: 1

• paddingdilation * (kernel_size - 1) - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padW,). Default: 0

• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padW). Default: 0

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

• dilation – the spacing between kernel elements. Can be a single number or a tuple (dW,). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50)
>>> weights = torch.randn(16, 33, 5)
>>> F.conv_transpose1d(inputs, weights)


### conv_transpose2d¶

torch.nn.functional.conv_transpose2d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 2D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose2d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iH , iW)$

• weight – filters of shape $(\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kH , kW)$

• bias – optional bias of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1

• paddingdilation * (kernel_size - 1) - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padH, padW). Default: 0

• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padH, out_padW). Default: 0

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

• dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1

Examples:

>>> # With square kernels and equal stride
>>> inputs = torch.randn(1, 4, 5, 5)
>>> weights = torch.randn(4, 8, 3, 3)


### conv_transpose3d¶

torch.nn.functional.conv_transpose3d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 3D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”

See ConvTranspose3d for details and output shape.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iT , iH , iW)$

• weight – filters of shape $(\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kT , kH , kW)$

• bias – optional bias of shape $(\text{out\_channels})$ . Default: None

• stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1

• paddingdilation * (kernel_size - 1) - padding zero-padding will be added to both sides of each dimension in the input. Can be a single number or a tuple (padT, padH, padW). Default: 0

• output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple (out_padT, out_padH, out_padW). Default: 0

• groups – split input into groups, $\text{in\_channels}$ should be divisible by the number of groups. Default: 1

• dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> weights = torch.randn(16, 33, 3, 3, 3)
>>> F.conv_transpose3d(inputs, weights)


### unfold¶

torch.nn.functional.unfold(input, kernel_size, dilation=1, padding=0, stride=1)[source]

Extracts sliding local blocks from an batched input tensor.

Warning

Currently, only 4-D input tensors (batched image-like tensors) are supported.

Warning

More than one element of the unfolded tensor may refer to a single memory location. As a result, in-place operations (especially ones that are vectorized) may result in incorrect behavior. If you need to write to the tensor, please clone it first.

See torch.nn.Unfold for details

### fold¶

torch.nn.functional.fold(input, output_size, kernel_size, dilation=1, padding=0, stride=1)[source]

Combines an array of sliding local blocks into a large containing tensor.

Warning

Currently, only 4-D output tensors (batched image-like tensors) are supported.

See torch.nn.Fold for details

## Pooling functions¶

### avg_pool1d¶

torch.nn.functional.avg_pool1d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor

Applies a 1D average pooling over an input signal composed of several input planes.

See AvgPool1d for details and output shape.

Parameters
• input – input tensor of shape $(\text{minibatch} , \text{in\_channels} , iW)$

• kernel_size – the size of the window. Can be a single number or a tuple (kW,)

• stride – the stride of the window. Can be a single number or a tuple (sW,). Default: kernel_size

• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padW,). Default: 0

• ceil_mode – when True, will use ceil instead of floor to compute the output shape. Default: False

• count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: True

Examples:

>>> # pool of square window of size=3, stride=2
>>> input = torch.tensor([[[1, 2, 3, 4, 5, 6, 7]]], dtype=torch.float32)
>>> F.avg_pool1d(input, kernel_size=3, stride=2)
tensor([[[ 2.,  4.,  6.]]])


### avg_pool2d¶

torch.nn.functional.avg_pool2d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True, divisor_override=None) → Tensor

Applies 2D average-pooling operation in $kH \times kW$ regions by step size $sH \times sW$ steps. The number of output features is equal to the number of input planes.

See AvgPool2d for details and output shape.

Parameters
• input – input tensor $(\text{minibatch} , \text{in\_channels} , iH , iW)$

• kernel_size – size of the pooling region. Can be a single number or a tuple (kH, kW)

• stride – stride of the pooling operation. Can be a single number or a tuple (sH, sW). Default: kernel_size

• padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0

• ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape. Default: False

• count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: True

• divisor_override – if specified, it will be used as divisor, otherwise size of the pooling region will be used. Default: None

### avg_pool3d¶

torch.nn.functional.avg_pool3d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True, divisor_override=None) → Tensor

Applies 3D average-pooling operation in $kT \times kH \times kW$ regions by step size $sT \times sH \times sW$ steps. The number of output features is equal to $\lfloor\frac{\text{input planes}}{sT}\rfloor$ .

See AvgPool3d for details and output shape.

Parameters
• input – input tensor $(\text{minibatch} , \text{in\_channels} , iT \times iH , iW)$

• kernel_size – size of the pooling region. Can be a single number or a tuple (kT, kH, kW)

• stride – stride of the pooling operation. Can be a single number or a tuple (sT, sH, sW). Default: kernel_size

• ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape

• count_include_pad – when True, will include the zero-padding in the averaging calculation

• divisor_override – if specified, it will be used as divisor, otherwise size of the pooling region will be used. Default: None

### max_pool1d¶

torch.nn.functional.max_pool1d(*args, **kwargs)

Applies a 1D max pooling over an input signal composed of several input planes.

See MaxPool1d for details.

### max_pool2d¶

torch.nn.functional.max_pool2d(*args, **kwargs)

Applies a 2D max pooling over an input signal composed of several input planes.

See MaxPool2d for details.

### max_pool3d¶

torch.nn.functional.max_pool3d(*args, **kwargs)

Applies a 3D max pooling over an input signal composed of several input planes.

See MaxPool3d for details.

### max_unpool1d¶

torch.nn.functional.max_unpool1d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool1d.

See MaxUnpool1d for details.

### max_unpool2d¶

torch.nn.functional.max_unpool2d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool2d.

See MaxUnpool2d for details.

### max_unpool3d¶

torch.nn.functional.max_unpool3d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool3d.

See MaxUnpool3d for details.

### lp_pool1d¶

torch.nn.functional.lp_pool1d(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]

Applies a 1D power-average pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.

See LPPool1d for details.

### lp_pool2d¶

torch.nn.functional.lp_pool2d(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]

Applies a 2D power-average pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.

See LPPool2d for details.

torch.nn.functional.adaptive_max_pool1d(*args, **kwargs)

Applies a 1D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool1d for details and output shape.

Parameters
• output_size – the target output size (single integer)

• return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_max_pool2d(*args, **kwargs)

Applies a 2D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool2d for details and output shape.

Parameters
• output_size – the target output size (single integer or double-integer tuple)

• return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_max_pool3d(*args, **kwargs)

Applies a 3D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool3d for details and output shape.

Parameters
• output_size – the target output size (single integer or triple-integer tuple)

• return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_avg_pool1d(input, output_size) → Tensor

Applies a 1D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool1d for details and output shape.

Parameters

output_size – the target output size (single integer)

torch.nn.functional.adaptive_avg_pool2d(input, output_size)[source]

Applies a 2D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool2d for details and output shape.

Parameters

output_size – the target output size (single integer or double-integer tuple)

torch.nn.functional.adaptive_avg_pool3d(input, output_size)[source]

Applies a 3D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool3d for details and output shape.

Parameters

output_size – the target output size (single integer or triple-integer tuple)

## Non-linear activation functions¶

### threshold¶

torch.nn.functional.threshold(input, threshold, value, inplace=False)[source]

Thresholds each element of the input Tensor.

See Threshold for more details.

torch.nn.functional.threshold_(input, threshold, value) → Tensor

In-place version of threshold().

### relu¶

torch.nn.functional.relu(input, inplace=False) → Tensor[source]

Applies the rectified linear unit function element-wise. See ReLU for more details.

torch.nn.functional.relu_(input) → Tensor

In-place version of relu().

### hardtanh¶

torch.nn.functional.hardtanh(input, min_val=-1., max_val=1., inplace=False) → Tensor[source]

Applies the HardTanh function element-wise. See Hardtanh for more details.

torch.nn.functional.hardtanh_(input, min_val=-1., max_val=1.) → Tensor

In-place version of hardtanh().

### relu6¶

torch.nn.functional.relu6(input, inplace=False) → Tensor[source]

Applies the element-wise function $\text{ReLU6}(x) = \min(\max(0,x), 6)$ .

See ReLU6 for more details.

### elu¶

torch.nn.functional.elu(input, alpha=1.0, inplace=False)[source]

Applies element-wise, $\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1))$ .

See ELU for more details.

torch.nn.functional.elu_(input, alpha=1.) → Tensor

In-place version of elu().

### selu¶

torch.nn.functional.selu(input, inplace=False) → Tensor[source]

Applies element-wise, $\text{SELU}(x) = scale * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))$ , with $\alpha=1.6732632423543772848170429916717$ and $scale=1.0507009873554804934193349852946$ .

See SELU for more details.

### celu¶

torch.nn.functional.celu(input, alpha=1., inplace=False) → Tensor[source]

Applies element-wise, $\text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha) - 1))$ .

See CELU for more details.

### leaky_relu¶

torch.nn.functional.leaky_relu(input, negative_slope=0.01, inplace=False) → Tensor[source]

Applies element-wise, $\text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x)$

See LeakyReLU for more details.

torch.nn.functional.leaky_relu_(input, negative_slope=0.01) → Tensor

In-place version of leaky_relu().

### prelu¶

torch.nn.functional.prelu(input, weight) → Tensor[source]

Applies element-wise the function $\text{PReLU}(x) = \max(0,x) + \text{weight} * \min(0,x)$ where weight is a learnable parameter.

See PReLU for more details.

### rrelu¶

torch.nn.functional.rrelu(input, lower=1./8, upper=1./3, training=False, inplace=False) → Tensor[source]

Randomized leaky ReLU.

See RReLU for more details.

torch.nn.functional.rrelu_(input, lower=1./8, upper=1./3, training=False) → Tensor

In-place version of rrelu().

### glu¶

torch.nn.functional.glu(input, dim=-1) → Tensor[source]

The gated linear unit. Computes:

$\text{GLU}(a, b) = a \otimes \sigma(b)$

where input is split in half along dim to form a and b, $\sigma$ is the sigmoid function and $\otimes$ is the element-wise product between matrices.

Parameters
• input (Tensor) – input tensor

• dim (int) – dimension on which to split the input. Default: -1

### gelu¶

torch.nn.functional.gelu(input) → Tensor[source]

Applies element-wise the function $\text{GeLU}(x) = x * \Phi(x)$

where $\Phi(x)$ is the Cumulative Distribution Function for Gaussian Distribution.

### logsigmoid¶

torch.nn.functional.logsigmoid(input) → Tensor

Applies element-wise $\text{LogSigmoid}(x_i) = \log \left(\frac{1}{1 + \exp(-x_i)}\right)$

See LogSigmoid for more details.

### hardshrink¶

torch.nn.functional.hardshrink(input, lambd=0.5) → Tensor[source]

Applies the hard shrinkage function element-wise

See Hardshrink for more details.

### tanhshrink¶

torch.nn.functional.tanhshrink(input) → Tensor[source]

Applies element-wise, $\text{Tanhshrink}(x) = x - \text{Tanh}(x)$

See Tanhshrink for more details.

### softsign¶

torch.nn.functional.softsign(input) → Tensor[source]

Applies element-wise, the function $\text{SoftSign}(x) = \frac{x}{1 + |x|}$

See Softsign for more details.

### softplus¶

torch.nn.functional.softplus(input, beta=1, threshold=20) → Tensor

### softmin¶

torch.nn.functional.softmin(input, dim=None, _stacklevel=3, dtype=None)[source]

Applies a softmin function.

Note that $\text{Softmin}(x) = \text{Softmax}(-x)$ . See softmax definition for mathematical formula.

See Softmin for more details.

Parameters
• input (Tensor) – input

• dim (int) – A dimension along which softmin will be computed (so every slice along dim will sum to 1).

• dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

### softmax¶

torch.nn.functional.softmax(input, dim=None, _stacklevel=3, dtype=None)[source]

Applies a softmax function.

Softmax is defined as:

$\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}$

It is applied to all slices along dim, and will re-scale them so that the elements lie in the range [0, 1] and sum to 1.

See Softmax for more details.

Parameters
• input (Tensor) – input

• dim (int) – A dimension along which softmax will be computed.

• dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

Note

This function doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use log_softmax instead (it’s faster and has better numerical properties).

### softshrink¶

torch.nn.functional.softshrink(input, lambd=0.5) → Tensor

Applies the soft shrinkage function elementwise

See Softshrink for more details.

### gumbel_softmax¶

torch.nn.functional.gumbel_softmax(logits, tau=1, hard=False, eps=1e-10, dim=-1)[source]

Samples from the Gumbel-Softmax distribution (Link 1 Link 2) and optionally discretizes.

Parameters
• logits[…, num_features] unnormalized log probabilities

• tau – non-negative scalar temperature

• hard – if True, the returned samples will be discretized as one-hot vectors, but will be differentiated as if it is the soft sample in autograd

• dim (int) – A dimension along which softmax will be computed. Default: -1.

Returns

Sampled tensor of same shape as logits from the Gumbel-Softmax distribution. If hard=True, the returned samples will be one-hot, otherwise they will be probability distributions that sum to 1 across dim.

Note

This function is here for legacy reasons, may be removed from nn.Functional in the future.

Note

The main trick for hard is to do y_hard - y_soft.detach() + y_soft

It achieves two things: - makes the output value exactly one-hot (since we add then subtract y_soft value) - makes the gradient equal to y_soft gradient (since we strip all other gradients)

Examples::
>>> logits = torch.randn(20, 32)
>>> # Sample soft categorical using reparametrization trick:
>>> F.gumbel_softmax(logits, tau=1, hard=False)
>>> # Sample hard categorical using "Straight-through" trick:
>>> F.gumbel_softmax(logits, tau=1, hard=True)


### log_softmax¶

torch.nn.functional.log_softmax(input, dim=None, _stacklevel=3, dtype=None)[source]

Applies a softmax followed by a logarithm.

While mathematically equivalent to log(softmax(x)), doing these two operations separately is slower, and numerically unstable. This function uses an alternative formulation to compute the output and gradient correctly.

See LogSoftmax for more details.

Parameters
• input (Tensor) – input

• dim (int) – A dimension along which log_softmax will be computed.

• dtype (torch.dtype, optional) – the desired data type of returned tensor. If specified, the input tensor is casted to dtype before the operation is performed. This is useful for preventing data type overflows. Default: None.

### tanh¶

torch.nn.functional.tanh(input) → Tensor[source]

Applies element-wise, $\text{Tanh}(x) = \tanh(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)}$

See Tanh for more details.

### sigmoid¶

torch.nn.functional.sigmoid(input) → Tensor[source]

Applies the element-wise function $\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)}$

See Sigmoid for more details.

## Normalization functions¶

### batch_norm¶

torch.nn.functional.batch_norm(input, running_mean, running_var, weight=None, bias=None, training=False, momentum=0.1, eps=1e-05)[source]

Applies Batch Normalization for each channel across a batch of data.

See BatchNorm1d, BatchNorm2d, BatchNorm3d for details.

### instance_norm¶

torch.nn.functional.instance_norm(input, running_mean=None, running_var=None, weight=None, bias=None, use_input_stats=True, momentum=0.1, eps=1e-05)[source]

Applies Instance Normalization for each channel in each data sample in a batch.

### layer_norm¶

torch.nn.functional.layer_norm(input, normalized_shape, weight=None, bias=None, eps=1e-05)[source]

Applies Layer Normalization for last certain number of dimensions.

See LayerNorm for details.

### local_response_norm¶

torch.nn.functional.local_response_norm(input, size, alpha=0.0001, beta=0.75, k=1.0)[source]

Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.

See LocalResponseNorm for details.

### normalize¶

torch.nn.functional.normalize(input, p=2, dim=1, eps=1e-12, out=None)[source]

Performs $L_p$ normalization of inputs over specified dimension.

For a tensor input of sizes $(n_0, ..., n_{dim}, ..., n_k)$ , each $n_{dim}$ -element vector $v$ along dimension dim is transformed as

$v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}.$

With the default arguments it uses the Euclidean norm over vectors along dimension $1$ for normalization.

Parameters
• input – input tensor of any shape

• p (float) – the exponent value in the norm formulation. Default: 2

• dim (int) – the dimension to reduce. Default: 1

• eps (float) – small value to avoid division by zero. Default: 1e-12

• out (Tensor, optional) – the output tensor. If out is used, this operation won’t be differentiable.

## Linear functions¶

### linear¶

torch.nn.functional.linear(input, weight, bias=None)[source]

Applies a linear transformation to the incoming data: $y = xA^T + b$ .

Shape:

• Input: $(N, *, in\_features)$ where * means any number of additional dimensions

• Weight: $(out\_features, in\_features)$

• Bias: $(out\_features)$

• Output: $(N, *, out\_features)$

### bilinear¶

torch.nn.functional.bilinear(input1, input2, weight, bias=None)[source]

Applies a bilinear transformation to the incoming data: $y = x_1 A x_2 + b$

Shape:

• input1: $(N, *, H_{in1})$ where $H_{in1}=\text{in1\_features}$ and $*$ means any number of additional dimensions. All but the last dimension of the inputs should be the same.

• input2: $(N, *, H_{in2})$ where $H_{in2}=\text{in2\_features}$

• weight: $(\text{out\_features}, \text{in1\_features}, \text{in2\_features})$

• bias: $(\text{out\_features})$

• output: $(N, *, H_{out})$ where $H_{out}=\text{out\_features}$ and all but the last dimension are the same shape as the input.

## Dropout functions¶

### dropout¶

torch.nn.functional.dropout(input, p=0.5, training=True, inplace=False)[source]

During training, randomly zeroes some of the elements of the input tensor with probability p using samples from a Bernoulli distribution.

See Dropout for details.

Parameters
• p – probability of an element to be zeroed. Default: 0.5

• training – apply dropout if is True. Default: True

• inplace – If set to True, will do this operation in-place. Default: False

### alpha_dropout¶

torch.nn.functional.alpha_dropout(input, p=0.5, training=False, inplace=False)[source]

Applies alpha dropout to the input.

See AlphaDropout for details.

### dropout2d¶

torch.nn.functional.dropout2d(input, p=0.5, training=True, inplace=False)[source]

Randomly zero out entire channels (a channel is a 2D feature map, e.g., the $j$ -th channel of the $i$ -th sample in the batched input is a 2D tensor $\text{input}[i, j]$ ) of the input tensor). Each channel will be zeroed out independently on every forward call with probability p using samples from a Bernoulli distribution.

See Dropout2d for details.

Parameters
• p – probability of a channel to be zeroed. Default: 0.5

• training – apply dropout if is True. Default: True

• inplace – If set to True, will do this operation in-place. Default: False

### dropout3d¶

torch.nn.functional.dropout3d(input, p=0.5, training=True, inplace=False)[source]

Randomly zero out entire channels (a channel is a 3D feature map, e.g., the $j$ -th channel of the $i$ -th sample in the batched input is a 3D tensor $\text{input}[i, j]$ ) of the input tensor). Each channel will be zeroed out independently on every forward call with probability p using samples from a Bernoulli distribution.

See Dropout3d for details.

Parameters
• p – probability of a channel to be zeroed. Default: 0.5

• training – apply dropout if is True. Default: True

• inplace – If set to True, will do this operation in-place. Default: False

## Sparse functions¶

### embedding¶

torch.nn.functional.embedding(input, weight, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False)[source]

A simple lookup table that looks up embeddings in a fixed dictionary and size.

This module is often used to retrieve word embeddings using indices. The input to the module is a list of indices, and the embedding matrix, and the output is the corresponding word embeddings.

See torch.nn.Embedding for more details.

Parameters
• input (LongTensor) – Tensor containing indices into the embedding matrix

• weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size

• padding_idx (int, optional) – If given, pads the output with the embedding vector at padding_idx (initialized to zeros) whenever it encounters the index.

• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm. Note: this will modify weight in-place.

• norm_type (float, optional) – The p of the p-norm to compute for the max_norm option. Default 2.

• scale_grad_by_freq (boolean, optional) – If given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False.

• sparse (bool, optional) – If True, gradient w.r.t. weight will be a sparse tensor. See Notes under torch.nn.Embedding for more details regarding sparse gradients.

Shape:
• Input: LongTensor of arbitrary shape containing the indices to extract

• Weight: Embedding matrix of floating point type with shape (V, embedding_dim),

where V = maximum index + 1 and embedding_dim = the embedding size

• Output: (*, embedding_dim), where * is the input shape

Examples:

>>> # a batch of 2 samples of 4 indices each
>>> input = torch.tensor([[1,2,4,5],[4,3,2,9]])
>>> # an embedding matrix containing 10 tensors of size 3
>>> embedding_matrix = torch.rand(10, 3)
>>> F.embedding(input, embedding_matrix)
tensor([[[ 0.8490,  0.9625,  0.6753],
[ 0.9666,  0.7761,  0.6108],
[ 0.6246,  0.9751,  0.3618],
[ 0.4161,  0.2419,  0.7383]],

[[ 0.6246,  0.9751,  0.3618],
[ 0.0237,  0.7794,  0.0528],
[ 0.9666,  0.7761,  0.6108],
[ 0.3385,  0.8612,  0.1867]]])

>>> weights = torch.rand(10, 3)
>>> weights[0, :].zero_()
>>> embedding_matrix = weights
>>> input = torch.tensor([[0,2,0,5]])
tensor([[[ 0.0000,  0.0000,  0.0000],
[ 0.5609,  0.5384,  0.8720],
[ 0.0000,  0.0000,  0.0000],
[ 0.6262,  0.2438,  0.7471]]])


### embedding_bag¶

torch.nn.functional.embedding_bag(input, weight, offsets=None, max_norm=None, norm_type=2, scale_grad_by_freq=False, mode='mean', sparse=False, per_sample_weights=None)[source]

Computes sums, means or maxes of bags of embeddings, without instantiating the intermediate embeddings.

See torch.nn.EmbeddingBag for more details.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters
• input (LongTensor) – Tensor containing bags of indices into the embedding matrix

• weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size

• offsets (LongTensor, optional) – Only used when input is 1D. offsets determines the starting index position of each bag (sequence) in input.

• max_norm (float, optional) – If given, each embedding vector with norm larger than max_norm is renormalized to have norm max_norm. Note: this will modify weight in-place.

• norm_type (float, optional) – The p in the p-norm to compute for the max_norm option. Default 2.

• scale_grad_by_freq (boolean, optional) – if given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default False. Note: this option is not supported when mode="max".

• mode (string, optional) – "sum", "mean" or "max". Specifies the way to reduce the bag. Default: "mean"

• sparse (bool, optional) – if True, gradient w.r.t. weight will be a sparse tensor. See Notes under torch.nn.Embedding for more details regarding sparse gradients. Note: this option is not supported when mode="max".

• per_sample_weights (Tensor, optional) – a tensor of float / double weights, or None to indicate all weights should be taken to be 1. If specified, per_sample_weights must have exactly the same shape as input and is treated as having the same offsets, if those are not None.

Shape:

• input (LongTensor) and offsets (LongTensor, optional)

• If input is 2D of shape (B, N),

it will be treated as B bags (sequences) each of fixed length N, and this will return B values aggregated in a way depending on the mode. offsets is ignored and required to be None in this case.

• If input is 1D of shape (N),

it will be treated as a concatenation of multiple bags (sequences). offsets is required to be a 1D tensor containing the starting index positions of each bag in input. Therefore, for offsets of shape (B), input will be viewed as having B bags. Empty bags (i.e., having 0-length) will have returned vectors filled by zeros.

• weight (Tensor): the learnable weights of the module of shape (num_embeddings, embedding_dim)

• per_sample_weights (Tensor, optional). Has the same shape as input.

• output: aggregated embedding values of shape (B, embedding_dim)

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding_matrix = torch.rand(10, 3)
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.tensor([1,2,4,5,4,3,2,9])
>>> offsets = torch.tensor([0,4])
>>> F.embedding_bag(embedding_matrix, input, offsets)
tensor([[ 0.3397,  0.3552,  0.5545],
[ 0.5893,  0.4386,  0.5882]])


### one_hot¶

torch.nn.functional.one_hot(tensor, num_classes=-1) → LongTensor

Takes LongTensor with index values of shape (*) and returns a tensor of shape (*, num_classes) that have zeros everywhere except where the index of last dimension matches the corresponding value of the input tensor, in which case it will be 1.

Parameters
• tensor (LongTensor) – class values of any shape.

• num_classes (int) – Total number of classes. If set to -1, the number of classes will be inferred as one greater than the largest class value in the input tensor.

Returns

LongTensor that has one more dimension with 1 values at the index of last dimension indicated by the input, and 0 everywhere else.

Examples

>>> F.one_hot(torch.arange(0, 5) % 3)
tensor([[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 0],
[0, 1, 0]])
>>> F.one_hot(torch.arange(0, 5) % 3, num_classes=5)
tensor([[1, 0, 0, 0, 0],
[0, 1, 0, 0, 0],
[0, 0, 1, 0, 0],
[1, 0, 0, 0, 0],
[0, 1, 0, 0, 0]])
>>> F.one_hot(torch.arange(0, 6).view(3,2) % 3)
tensor([[[1, 0, 0],
[0, 1, 0]],
[[0, 0, 1],
[1, 0, 0]],
[[0, 1, 0],
[0, 0, 1]]])


## Distance functions¶

### pairwise_distance¶

torch.nn.functional.pairwise_distance(x1, x2, p=2.0, eps=1e-06, keepdim=False)[source]

See torch.nn.PairwiseDistance for details

### cosine_similarity¶

torch.nn.functional.cosine_similarity(x1, x2, dim=1, eps=1e-8) → Tensor

Returns cosine similarity between x1 and x2, computed along dim.

$\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}$
Parameters
• x1 (Tensor) – First input.

• x2 (Tensor) – Second input (of size matching x1).

• dim (int, optional) – Dimension of vectors. Default: 1

• eps (float, optional) – Small value to avoid division by zero. Default: 1e-8

Shape:
• Input: $(\ast_1, D, \ast_2)$ where D is at position dim.

• Output: $(\ast_1, \ast_2)$ where 1 is at position dim.

Example:

>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = F.cosine_similarity(input1, input2)
>>> print(output)


### pdist¶

torch.nn.functional.pdist(input, p=2) → Tensor

Computes the p-norm distance between every pair of row vectors in the input. This is identical to the upper triangular portion, excluding the diagonal, of torch.norm(input[:, None] - input, dim=2, p=p). This function will be faster if the rows are contiguous.

If input has shape $N \times M$ then the output will have shape $\frac{1}{2} N (N - 1)$ .

This function is equivalent to scipy.spatial.distance.pdist(input, ‘minkowski’, p=p) if $p \in (0, \infty)$ . When $p = 0$ it is equivalent to scipy.spatial.distance.pdist(input, ‘hamming’) * M. When $p = \infty$ , the closest scipy function is scipy.spatial.distance.pdist(xn, lambda x, y: np.abs(x - y).max()).

Parameters
• input – input tensor of shape $N \times M$ .

• p – p value for the p-norm distance to calculate between each vector pair $\in [0, \infty]$ .

## Loss functions¶

### binary_cross_entropy¶

torch.nn.functional.binary_cross_entropy(input, target, weight=None, size_average=None, reduce=None, reduction='mean')[source]

Function that measures the Binary Cross Entropy between the target and the output.

See BCELoss for details.

Parameters
• input – Tensor of arbitrary shape

• target – Tensor of the same shape as input

• weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

Examples:

>>> input = torch.randn((3, 2), requires_grad=True)
>>> target = torch.rand((3, 2), requires_grad=False)
>>> loss = F.binary_cross_entropy(F.sigmoid(input), target)
>>> loss.backward()


### binary_cross_entropy_with_logits¶

torch.nn.functional.binary_cross_entropy_with_logits(input, target, weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)[source]

Function that measures Binary Cross Entropy between target and output logits.

See BCEWithLogitsLoss for details.

Parameters
• input – Tensor of arbitrary shape

• target – Tensor of the same shape as input

• weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

• pos_weight (Tensor, optional) – a weight of positive examples. Must be a vector with length equal to the number of classes.

Examples:

>>> input = torch.randn(3, requires_grad=True)
>>> target = torch.empty(3).random_(2)
>>> loss = F.binary_cross_entropy_with_logits(input, target)
>>> loss.backward()


### poisson_nll_loss¶

torch.nn.functional.poisson_nll_loss(input, target, log_input=True, full=False, size_average=None, eps=1e-08, reduce=None, reduction='mean')[source]

Poisson negative log likelihood loss.

See PoissonNLLLoss for details.

Parameters
• input – expectation of underlying Poisson distribution.

• target – random sample $target \sim \text{Poisson}(input)$ .

• log_input – if True the loss is computed as $\exp(\text{input}) - \text{target} * \text{input}$ , if False then loss is $\text{input} - \text{target} * \log(\text{input}+\text{eps})$ . Default: True

• full – whether to compute full loss, i. e. to add the Stirling approximation term. Default: False $\text{target} * \log(\text{target}) - \text{target} + 0.5 * \log(2 * \pi * \text{target})$ .

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• eps (float, optional) – Small value to avoid evaluation of $\log(0)$ when log_input=False. Default: 1e-8

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

### cosine_embedding_loss¶

torch.nn.functional.cosine_embedding_loss(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor[source]

See CosineEmbeddingLoss for details.

### cross_entropy¶

torch.nn.functional.cross_entropy(input, target, weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')[source]

This criterion combines log_softmax and nll_loss in a single function.

See CrossEntropyLoss for details.

Parameters
• input (Tensor) – $(N, C)$ where C = number of classes or $(N, C, H, W)$ in case of 2D Loss, or $(N, C, d_1, d_2, ..., d_K)$ where $K \geq 1$ in the case of K-dimensional loss.

• target (Tensor) – $(N)$ where each value is $0 \leq \text{targets}[i] \leq C-1$ , or $(N, d_1, d_2, ..., d_K)$ where $K \geq 1$ for K-dimensional loss.

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

Examples:

>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randint(5, (3,), dtype=torch.int64)
>>> loss = F.cross_entropy(input, target)
>>> loss.backward()


### ctc_loss¶

torch.nn.functional.ctc_loss(log_probs, targets, input_lengths, target_lengths, blank=0, reduction='mean', zero_infinity=False)[source]

The Connectionist Temporal Classification loss.

See CTCLoss for details.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = True. Please see the notes on Reproducibility for background.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters
• log_probs$(T, N, C)$ where C = number of characters in alphabet including blank, T = input length, and N = batch size. The logarithmized probabilities of the outputs (e.g. obtained with torch.nn.functional.log_softmax()).

• targets$(N, S)$ or (sum(target_lengths)). Targets cannot be blank. In the second form, the targets are assumed to be concatenated.

• input_lengths$(N)$ . Lengths of the inputs (must each be $\leq T$ )

• target_lengths$(N)$ . Lengths of the targets

• blank (int, optional) – Blank label. Default $0$ .

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the output losses will be divided by the target lengths and then the mean over the batch is taken, 'sum': the output will be summed. Default: 'mean'

• zero_infinity (bool, optional) – Whether to zero infinite losses and the associated gradients. Default: False Infinite losses mainly occur when the inputs are too short to be aligned to the targets.

Example:

>>> log_probs = torch.randn(50, 16, 20).log_softmax(2).detach().requires_grad_()
>>> targets = torch.randint(1, 20, (16, 30), dtype=torch.long)
>>> input_lengths = torch.full((16,), 50, dtype=torch.long)
>>> target_lengths = torch.randint(10,30,(16,), dtype=torch.long)
>>> loss = F.ctc_loss(log_probs, targets, input_lengths, target_lengths)
>>> loss.backward()


### hinge_embedding_loss¶

torch.nn.functional.hinge_embedding_loss(input, target, margin=1.0, size_average=None, reduce=None, reduction='mean') → Tensor[source]

See HingeEmbeddingLoss for details.

### kl_div¶

torch.nn.functional.kl_div(input, target, size_average=None, reduce=None, reduction='mean')[source]

The Kullback-Leibler divergence_ Loss.

See KLDivLoss for details.

Parameters
• input – Tensor of arbitrary shape

• target – Tensor of the same shape as input

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'batchmean' | 'sum' | 'mean'. 'none': no reduction will be applied 'batchmean': the sum of the output will be divided by the batchsize 'sum': the output will be summed 'mean': the output will be divided by the number of elements in the output Default: 'mean'

Note

size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction.

Note

:attr:reduction = 'mean' doesn’t return the true kl divergence value, please use :attr:reduction = 'batchmean' which aligns with KL math definition. In the next major release, 'mean' will be changed to be the same as ‘batchmean’.

### l1_loss¶

torch.nn.functional.l1_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor[source]

Function that takes the mean element-wise absolute value difference.

See L1Loss for details.

### mse_loss¶

torch.nn.functional.mse_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor[source]

Measures the element-wise mean squared error.

See MSELoss for details.

### margin_ranking_loss¶

torch.nn.functional.margin_ranking_loss(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor[source]

See MarginRankingLoss for details.

### multilabel_margin_loss¶

torch.nn.functional.multilabel_margin_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor[source]

See MultiLabelMarginLoss for details.

### multilabel_soft_margin_loss¶

torch.nn.functional.multilabel_soft_margin_loss(input, target, weight=None, size_average=None) → Tensor[source]

See MultiLabelSoftMarginLoss for details.

### multi_margin_loss¶

torch.nn.functional.multi_margin_loss(input, target, p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')[source]
multi_margin_loss(input, target, p=1, margin=1, weight=None, size_average=None,

reduce=None, reduction=’mean’) -> Tensor

See MultiMarginLoss for details.

### nll_loss¶

torch.nn.functional.nll_loss(input, target, weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')[source]

The negative log likelihood loss.

See NLLLoss for details.

Parameters
• input$(N, C)$ where C = number of classes or $(N, C, H, W)$ in case of 2D Loss, or $(N, C, d_1, d_2, ..., d_K)$ where $K \geq 1$ in the case of K-dimensional loss.

• target$(N)$ where each value is $0 \leq \text{targets}[i] \leq C-1$ , or $(N, d_1, d_2, ..., d_K)$ where $K \geq 1$ for K-dimensional loss.

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

Example:

>>> # input is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> output = F.nll_loss(F.log_softmax(input), target)
>>> output.backward()


### smooth_l1_loss¶

torch.nn.functional.smooth_l1_loss(input, target, size_average=None, reduce=None, reduction='mean')[source]

Function that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise.

See SmoothL1Loss for details.

### soft_margin_loss¶

torch.nn.functional.soft_margin_loss(input, target, size_average=None, reduce=None, reduction='mean') → Tensor[source]

See SoftMarginLoss for details.

### triplet_margin_loss¶

torch.nn.functional.triplet_margin_loss(anchor, positive, negative, margin=1.0, p=2, eps=1e-06, swap=False, size_average=None, reduce=None, reduction='mean')[source]

See TripletMarginLoss for details

## Vision functions¶

### pixel_shuffle¶

torch.nn.functional.pixel_shuffle()

Rearranges elements in a tensor of shape $(*, C \times r^2, H, W)$ to a tensor of shape $(*, C, H \times r, W \times r)$ .

See PixelShuffle for details.

Parameters
• input (Tensor) – the input tensor

• upscale_factor (int) – factor to increase spatial resolution by

Examples:

>>> input = torch.randn(1, 9, 4, 4)
>>> output = torch.nn.functional.pixel_shuffle(input, 3)
>>> print(output.size())
torch.Size([1, 1, 12, 12])


torch.nn.functional.pad(input, pad, mode='constant', value=0)[source]

The padding size by which to pad some dimensions of input are described starting from the last dimension and moving forward. $\left\lfloor\frac{\text{len(pad)}}{2}\right\rfloor$ dimensions of input will be padded. For example, to pad only the last dimension of the input tensor, then pad has the form $(\text{padding\_left}, \text{padding\_right})$ ; to pad the last 2 dimensions of the input tensor, then use $(\text{padding\_left}, \text{padding\_right},$ $\text{padding\_top}, \text{padding\_bottom})$ ; to pad the last 3 dimensions, use $(\text{padding\_left}, \text{padding\_right},$ $\text{padding\_top}, \text{padding\_bottom}$ $\text{padding\_front}, \text{padding\_back})$ .

See torch.nn.ConstantPad2d, torch.nn.ReflectionPad2d, and torch.nn.ReplicationPad2d for concrete examples on how each of the padding modes works. Constant padding is implemented for arbitrary dimensions. Replicate padding is implemented for padding the last 3 dimensions of 5D input tensor, or the last 2 dimensions of 4D input tensor, or the last dimension of 3D input tensor. Reflect padding is only implemented for padding the last 2 dimensions of 4D input tensor, or the last dimension of 3D input tensor.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters
• input (Tensor) – N-dimensional tensor

• pad (tuple) – m-elements tuple, where $\frac{m}{2} \leq$ input dimensions and $m$ is even.

• mode'constant', 'reflect', 'replicate' or 'circular'. Default: 'constant'

• value – fill value for 'constant' padding. Default: 0

Examples:

>>> t4d = torch.empty(3, 3, 4, 2)
>>> p1d = (1, 1) # pad last dim by 1 on each side
>>> print(out.data.size())
torch.Size([3, 3, 4, 4])
>>> p2d = (1, 1, 2, 2) # pad last dim by (1, 1) and 2nd to last by (2, 2)
>>> out = F.pad(t4d, p2d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 3, 8, 4])
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p3d = (0, 1, 2, 1, 3, 3) # pad by (0, 1), (2, 1), and (3, 3)
>>> out = F.pad(t4d, p3d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 9, 7, 3])


### interpolate¶

torch.nn.functional.interpolate(input, size=None, scale_factor=None, mode='nearest', align_corners=None)[source]

Down/up samples the input to either the given size or the given scale_factor

The algorithm used for interpolation is determined by mode.

Currently temporal, spatial and volumetric sampling are supported, i.e. expected inputs are 3-D, 4-D or 5-D in shape.

The input dimensions are interpreted in the form: mini-batch x channels x [optional depth] x [optional height] x width.

The modes available for resizing are: nearest, linear (3D-only), bilinear, bicubic (4D-only), trilinear (5D-only), area

Parameters
• input (Tensor) – the input tensor

• size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int]) – output spatial size.

• scale_factor (float or Tuple[float]) – multiplier for spatial size. Has to match input size if it is a tuple.

• mode (str) – algorithm used for upsampling: 'nearest' | 'linear' | 'bilinear' | 'bicubic' | 'trilinear' | 'area'. Default: 'nearest'

• align_corners (bool, optional) – Geometrically, we consider the pixels of the input and output as squares rather than points. If set to True, the input and output tensors are aligned by the center points of their corner pixels, preserving the values at the corner pixels. If set to False, the input and output tensors are aligned by the corner points of their corner pixels, and the interpolation uses edge value padding for out-of-boundary values, making this operation independent of input size when scale_factor is kept the same. This only has an effect when mode is 'linear', 'bilinear', 'bicubic' or 'trilinear'. Default: False

Note

With mode='bicubic', it’s possible to cause overshoot, in other words it can produce negative values or values greater than 255 for images. Explicitly call result.clamp(min=0, max=255) if you want to reduce the overshoot when displaying the image.

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See Upsample for concrete examples on how this affects the outputs.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

### upsample¶

torch.nn.functional.upsample(input, size=None, scale_factor=None, mode='nearest', align_corners=None)[source]

Upsamples the input to either the given size or the given scale_factor

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(...).

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

The algorithm used for upsampling is determined by mode.

Currently temporal, spatial and volumetric upsampling are supported, i.e. expected inputs are 3-D, 4-D or 5-D in shape.

The input dimensions are interpreted in the form: mini-batch x channels x [optional depth] x [optional height] x width.

The modes available for upsampling are: nearest, linear (3D-only), bilinear, bicubic (4D-only), trilinear (5D-only)

Parameters
• input (Tensor) – the input tensor

• size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int]) – output spatial size.

• scale_factor (float or Tuple[float]) – multiplier for spatial size. Has to be an integer.

• mode (string) – algorithm used for upsampling: 'nearest' | 'linear' | 'bilinear' | 'bicubic' | 'trilinear'. Default: 'nearest'

• align_corners (bool, optional) – Geometrically, we consider the pixels of the input and output as squares rather than points. If set to True, the input and output tensors are aligned by the center points of their corner pixels, preserving the values at the corner pixels. If set to False, the input and output tensors are aligned by the corner points of their corner pixels, and the interpolation uses edge value padding for out-of-boundary values, making this operation independent of input size when scale_factor is kept the same. This only has an effect when mode is 'linear', 'bilinear', 'bicubic' or 'trilinear'. Default: False

Note

With mode='bicubic', it’s possible to cause overshoot, in other words it can produce negative values or values greater than 255 for images. Explicitly call result.clamp(min=0, max=255) if you want to reduce the overshoot when displaying the image.

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See Upsample for concrete examples on how this affects the outputs.

### upsample_nearest¶

torch.nn.functional.upsample_nearest(input, size=None, scale_factor=None)[source]

Upsamples the input, using nearest neighbours’ pixel values.

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(..., mode='nearest').

Currently spatial and volumetric upsampling are supported (i.e. expected inputs are 4 or 5 dimensional).

Parameters
• input (Tensor) – input

• size (int or Tuple[int, int] or Tuple[int, int, int]) – output spatia size.

• scale_factor (int) – multiplier for spatial size. Has to be an integer.

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

### upsample_bilinear¶

torch.nn.functional.upsample_bilinear(input, size=None, scale_factor=None)[source]

Upsamples the input, using bilinear upsampling.

Warning

This function is deprecated in favor of torch.nn.functional.interpolate(). This is equivalent with nn.functional.interpolate(..., mode='bilinear', align_corners=True).

Expected inputs are spatial (4 dimensional). Use upsample_trilinear fo volumetric (5 dimensional) inputs.

Parameters
• input (Tensor) – input

• size (int or Tuple[int, int]) – output spatial size.

• scale_factor (int or Tuple[int, int]) – multiplier for spatial size

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

### grid_sample¶

torch.nn.functional.grid_sample(input, grid, mode='bilinear', padding_mode='zeros', align_corners=None)[source]

Given an input and a flow-field grid, computes the output using input values and pixel locations from grid.

Currently, only spatial (4-D) and volumetric (5-D) input are supported.

In the spatial (4-D) case, for input with shape $(N, C, H_\text{in}, W_\text{in})$ and grid with shape $(N, H_\text{out}, W_\text{out}, 2)$ , the output will have shape $(N, C, H_\text{out}, W_\text{out})$ .

For each output location output[n, :, h, w], the size-2 vector grid[n, h, w] specifies input pixel locations x and y, which are used to interpolate the output value output[n, :, h, w]. In the case of 5D inputs, grid[n, d, h, w] specifies the x, y, z pixel locations for interpolating output[n, :, d, h, w]. mode argument specifies nearest or bilinear interpolation method to sample the input pixels.

grid specifies the sampling pixel locations normalized by the input spatial dimensions. Therefore, it should have most values in the range of [-1, 1]. For example, values x = -1, y = -1 is the left-top pixel of input, and values x = 1, y = 1 is the right-bottom pixel of input.

If grid has values outside the range of [-1, 1], the corresponding outputs are handled as defined by padding_mode. Options are

• padding_mode="zeros": use 0 for out-of-bound grid locations,

• padding_mode="border": use border values for out-of-bound grid locations,

• padding_mode="reflection": use values at locations reflected by the border for out-of-bound grid locations. For location far away from the border, it will keep being reflected until becoming in bound, e.g., (normalized) pixel location x = -3.5 reflects by border -1 and becomes x' = 1.5, then reflects by border 1 and becomes x'' = -0.5.

Note

This function is often used in conjunction with affine_grid() to build Spatial Transformer Networks .

Note

When using the CUDA backend, this operation may induce nondeterministic behaviour in its backward pass that is not easily switched off. Please see the notes on Reproducibility for background.

Parameters
• input (Tensor) – input of shape $(N, C, H_\text{in}, W_\text{in})$ (4-D case) or $(N, C, D_\text{in}, H_\text{in}, W_\text{in})$ (5-D case)

• grid (Tensor) – flow-field of shape $(N, H_\text{out}, W_\text{out}, 2)$ (4-D case) or $(N, D_\text{out}, H_\text{out}, W_\text{out}, 3)$ (5-D case)

• mode (str) – interpolation mode to calculate output values 'bilinear' | 'nearest'. Default: 'bilinear'

• padding_mode (str) – padding mode for outside grid values 'zeros' | 'border' | 'reflection'. Default: 'zeros'

• align_corners (bool, optional) – Geometrically, we consider the pixels of the input as squares rather than points. If set to True, the extrema (-1 and 1) are considered as referring to the center points of the input’s corner pixels. If set to False, they are instead considered as referring to the corner points of the input’s corner pixels, making the sampling more resolution agnostic. This option parallels the align_corners option in interpolate(), and so whichever option is used here should also be used there to resize the input image before grid sampling. Default: False

Returns

output Tensor

Return type

output (Tensor)

Warning

When align_corners = True, the grid positions depend on the pixel size relative to the input image size, and so the locations sampled by grid_sample() will differ for the same input given at different resolutions (that is, after being upsampled or downsampled). The default behavior up to version 1.2.0 was align_corners = True. Since then, the default behavior has been changed to align_corners = False, in order to bring it in line with the default for interpolate().

### affine_grid¶

torch.nn.functional.affine_grid(theta, size, align_corners=None)[source]

Generates a 2D or 3D flow field (sampling grid), given a batch of affine matrices theta.

Note

This function is often used in conjunction with grid_sample() to build Spatial Transformer Networks .

Parameters
• theta (Tensor) – input batch of affine matrices with shape ($N \times 2 \times 3$ ) for 2D or ($N \times 3 \times 4$ ) for 3D

• size (torch.Size) – the target output image size. ($N \times C \times H \times W$ for 2D or $N \times C \times D \times H \times W$ for 3D) Example: torch.Size((32, 3, 24, 24))

• align_corners (bool, optional) – if True, consider -1 and 1 to refer to the centers of the corner pixels rather than the image corners. Refer to grid_sample() for a more complete description. A grid generated by affine_grid() should be passed to grid_sample() with the same setting for this option. Default: False

Returns

output Tensor of size ($N \times H \times W \times 2$ )

Return type

output (Tensor)

Warning

When align_corners = True, the grid positions depend on the pixel size relative to the input image size, and so the locations sampled by grid_sample() will differ for the same input given at different resolutions (that is, after being upsampled or downsampled). The default behavior up to version 1.2.0 was align_corners = True. Since then, the default behavior has been changed to align_corners = False, in order to bring it in line with the default for interpolate().

Warning

When align_corners = True, 2D affine transforms on 1D data and 3D affine transforms on 2D data (that is, when one of the spatial dimensions has unit size) are ill-defined, and not an intended use case. This is not a problem when align_corners = False. Up to version 1.2.0, all grid points along a unit dimension were considered arbitrarily to be at -1. From version 1.3.0, under align_corners = True all grid points along a unit dimension are condsidered to be at 0 (the center of the input image).

## DataParallel functions (multi-GPU, distributed)¶

### data_parallel¶

torch.nn.parallel.data_parallel`(module, inputs, device_ids=None, output_device=None, dim=0, module_kwargs=None)[source]

Evaluates module(input) in parallel across the GPUs given in device_ids.

This is the functional version of the DataParallel module.

Parameters
• module (Module) – the module to evaluate in parallel

• inputs (Tensor) – inputs to the module

• device_ids (list of python:int or torch.device) – GPU ids on which to replicate module

• output_device (list of python:int or torch.device) – GPU location of the output Use -1 to indicate the CPU. (default: device_ids[0])

Returns

a Tensor containing the result of module(input) located on output_device