torch.nn.init

Created On: Jun 11, 2019 | Last Updated On: Jul 07, 2022

Warning

All the functions in this module are intended to be used to initialize neural network parameters, so they all run in torch.no_grad() mode and will not be taken into account by autograd.

torch.nn.init.calculate_gain(nonlinearity, param=None)

Return the recommended gain value for the given nonlinearity function.

The values are as follows:

nonlinearity	gain
Linear / Identity	$1$
Conv{1,2,3}D	$1$
Sigmoid	$1$
Tanh	$\frac{5}{3}$
ReLU	$\sqrt{2}$
Leaky Relu	$\sqrt{\frac{2}{1+{\text{negative\_slope}}^2}}$
SELU	$\frac{3}{4}$

Warning

In order to implement Self-Normalizing Neural Networks , you should use nonlinearity='linear' instead of nonlinearity='selu'. This gives the initial weights a variance of 1 / N, which is necessary to induce a stable fixed point in the forward pass. In contrast, the default gain for SELU sacrifices the normalization effect for more stable gradient flow in rectangular layers.

Parameters

• nonlinearity (Literal['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d', 'sigmoid', 'tanh', 'relu', 'leaky_relu', 'selu']) – the non-linear function (nn.functional name)

• param (Optional[Union[int, float]]) – optional parameter for the non-linear function

Return type

float

Examples

>>> gain = nn.init.calculate_gain(
...     "leaky_relu", 0.2
... )  # leaky_relu with negative_slope=0.2

torch.nn.init.uniform_(tensor, a=0.0, b=1.0, generator=None)

Fill the input Tensor with values drawn from the uniform distribution.

$\mathcal{U}(a,b)$.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• a (float) – the lower bound of the uniform distribution

• b (float) – the upper bound of the uniform distribution

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.uniform_(w)

torch.nn.init.normal_(tensor, mean=0.0, std=1.0, generator=None)

Fill the input Tensor with values drawn from the normal distribution.

$\mathcal{N}(\text{mean},{\text{std}}^2)$.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• mean (float) – the mean of the normal distribution

• std (float) – the standard deviation of the normal distribution

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.normal_(w)

torch.nn.init.constant_(tensor, val)

Fill the input Tensor with the value $\text{val}$.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• val (float) – the value to fill the tensor with

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.constant_(w, 0.3)

torch.nn.init.ones_(tensor)

Fill the input Tensor with the scalar value 1.

Parameters

tensor (Tensor) – an n-dimensional torch.Tensor

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.ones_(w)

torch.nn.init.zeros_(tensor)

Fill the input Tensor with the scalar value 0.

Parameters

tensor (Tensor) – an n-dimensional torch.Tensor

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.zeros_(w)

torch.nn.init.eye_(tensor)

Fill the 2-dimensional input Tensor with the identity matrix.

Preserves the identity of the inputs in Linear layers, where as many inputs are preserved as possible.

Parameters

tensor (Tensor) – a 2-dimensional torch.Tensor

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.eye_(w)

torch.nn.init.dirac_(tensor, groups=1)

Fill the {3, 4, 5}-dimensional input Tensor with the Dirac delta function.

Preserves the identity of the inputs in Convolutional layers, where as many input channels are preserved as possible. In case of groups>1, each group of channels preserves identity

Parameters

• tensor (Tensor) – a {3, 4, 5}-dimensional torch.Tensor

• groups (int, optional) – number of groups in the conv layer (default: 1)

Return type

Tensor

Examples

>>> w = torch.empty(3, 16, 5, 5)
>>> nn.init.dirac_(w)
>>> w = torch.empty(3, 24, 5, 5)
>>> nn.init.dirac_(w, 3)

torch.nn.init.xavier_uniform_(tensor, gain=1.0, generator=None)

Fill the input Tensor with values using a Xavier uniform distribution.

The method is described in Understanding the difficulty of training deep feedforward neural networks - Glorot, X. & Bengio, Y. (2010). The resulting tensor will have values sampled from $\mathcal{U}(-a,a)$ where

$$a=\text{gain}\times \sqrt{\frac{6}{\text{fan\_in}+\text{fan\_out}}}$$

Also known as Glorot initialization.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• gain (float) – an optional scaling factor

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain("relu"))

torch.nn.init.xavier_normal_(tensor, gain=1.0, generator=None)

Fill the input Tensor with values using a Xavier normal distribution.

The method is described in Understanding the difficulty of training deep feedforward neural networks - Glorot, X. & Bengio, Y. (2010). The resulting tensor will have values sampled from $\mathcal{N}(0,{\text{std}}^2)$ where

$$\text{std}=\text{gain}\times \sqrt{\frac{2}{\text{fan\_in}+\text{fan\_out}}}$$

Also known as Glorot initialization.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• gain (float) – an optional scaling factor

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_normal_(w)

torch.nn.init.kaiming_uniform_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu', generator=None)

Fill the input Tensor with values using a Kaiming uniform distribution.

The method is described in Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification - He, K. et al. (2015). The resulting tensor will have values sampled from $\mathcal{U}(-\text{bound},\text{bound})$ where

$$\text{bound}=\text{gain}\times \sqrt{\frac{3}{\text{fan\_mode}}}$$

Also known as He initialization.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• a (float) – the negative slope of the rectifier used after this layer (only used with 'leaky_relu')

• mode (Literal['fan_in', 'fan_out']) – either 'fan_in' (default) or 'fan_out'. Choosing 'fan_in' preserves the magnitude of the variance of the weights in the forward pass. Choosing 'fan_out' preserves the magnitudes in the backwards pass.

• nonlinearity (Literal['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d', 'sigmoid', 'tanh', 'relu', 'leaky_relu', 'selu']) – the non-linear function (nn.functional name), recommended to use only with 'relu' or 'leaky_relu' (default).

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_uniform_(w, mode="fan_in", nonlinearity="relu")

Note

Be aware that fan_in and fan_out are calculated assuming that the weight matrix is used in a transposed manner, (i.e., x @ w.T in Linear layers, where w.shape = [fan_out, fan_in]). This is important for correct initialization. If you plan to use x @ w, where w.shape = [fan_in, fan_out], pass in a transposed weight matrix, i.e. nn.init.kaiming_uniform_(w.T, ...).

torch.nn.init.kaiming_normal_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu', generator=None)

Fill the input Tensor with values using a Kaiming normal distribution.

The method is described in Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification - He, K. et al. (2015). The resulting tensor will have values sampled from $\mathcal{N}(0,{\text{std}}^2)$ where

$$\text{std}=\frac{\text{gain}}{\sqrt{\text{fan\_mode}}}$$

Also known as He initialization.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• a (float) – the negative slope of the rectifier used after this layer (only used with 'leaky_relu')

• mode (Literal['fan_in', 'fan_out']) – either 'fan_in' (default) or 'fan_out'. Choosing 'fan_in' preserves the magnitude of the variance of the weights in the forward pass. Choosing 'fan_out' preserves the magnitudes in the backwards pass.

• nonlinearity (Literal['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d', 'sigmoid', 'tanh', 'relu', 'leaky_relu', 'selu']) – the non-linear function (nn.functional name), recommended to use only with 'relu' or 'leaky_relu' (default).

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_normal_(w, mode="fan_out", nonlinearity="relu")

Note

Be aware that fan_in and fan_out are calculated assuming that the weight matrix is used in a transposed manner, (i.e., x @ w.T in Linear layers, where w.shape = [fan_out, fan_in]). This is important for correct initialization. If you plan to use x @ w, where w.shape = [fan_in, fan_out], pass in a transposed weight matrix, i.e. nn.init.kaiming_normal_(w.T, ...).

torch.nn.init.trunc_normal_(tensor, mean=0.0, std=1.0, a=-2.0, b=2.0, generator=None)

Fill the input Tensor with values drawn from a truncated normal distribution.

The values are effectively drawn from the normal distribution $\mathcal{N}(\text{mean},{\text{std}}^2)$ with values outside $[a,b]$ redrawn until they are within the bounds. The method used for generating the random values works best when $a\le \text{mean}\le b$.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• mean (float) – the mean of the normal distribution

• std (float) – the standard deviation of the normal distribution

• a (float) – the minimum cutoff value

• b (float) – the maximum cutoff value

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.trunc_normal_(w)

torch.nn.init.orthogonal_(tensor, gain=1, generator=None)

Fill the input Tensor with a (semi) orthogonal matrix.

Described in Exact solutions to the nonlinear dynamics of learning in deep linear neural networks - Saxe, A. et al. (2013). The input tensor must have at least 2 dimensions, and for tensors with more than 2 dimensions the trailing dimensions are flattened.

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor, where $n\ge 2$

• gain (float) – optional scaling factor

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.orthogonal_(w)

torch.nn.init.sparse_(tensor, sparsity, std=0.01, generator=None)

Fill the 2D input Tensor as a sparse matrix.

The non-zero elements will be drawn from the normal distribution $\mathcal{N}(0,0.01)$, as described in Deep learning via Hessian-free optimization - Martens, J. (2010).

Parameters

• tensor (Tensor) – an n-dimensional torch.Tensor

• sparsity (float) – The fraction of elements in each column to be set to zero

• std (float) – the standard deviation of the normal distribution used to generate the non-zero values

• generator (Optional[Generator]) – the torch Generator to sample from (default: None)

Return type

Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.sparse_(w, sparsity=0.1)