torch.nn.init

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 normalisation effect for more stable gradient flow in rectangular layers.

Parameters

• nonlinearity – the non-linear function (nn.functional name)

• param – optional parameter for the non-linear function

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)

Fills the input Tensor with values drawn from the uniform distribution $\mathcal{U}(a, b)$.

Parameters

• tensor – an n-dimensional torch.Tensor

• a – the lower bound of the uniform distribution

• b – the upper bound of the uniform distribution

Examples

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

torch.nn.init.normal_(tensor, mean=0.0, std=1.0)

Fills the input Tensor with values drawn from the normal distribution $\mathcal{N}(\text{mean}, \text{std}^2)$.

Parameters

• tensor – an n-dimensional torch.Tensor

• mean – the mean of the normal distribution

• std – the standard deviation of the normal distribution

Examples

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

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

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

Parameters

• tensor – an n-dimensional torch.Tensor

• val – the value to fill the tensor with

Examples

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

torch.nn.init.ones_(tensor)

Fills the input Tensor with the scalar value 1.

Parameters

tensor – an n-dimensional torch.Tensor

Examples

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

torch.nn.init.zeros_(tensor)

Fills the input Tensor with the scalar value 0.

Parameters

tensor – an n-dimensional torch.Tensor

Examples

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

torch.nn.init.eye_(tensor)

Fills 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 – a 2-dimensional torch.Tensor

Examples

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

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

Fills 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 – a {3, 4, 5}-dimensional torch.Tensor

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

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)

Fills the input Tensor with values according to the method described in Understanding the difficulty of training deep feedforward neural networks - Glorot, X. & Bengio, Y. (2010), using a uniform distribution. 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 – an n-dimensional torch.Tensor

• gain – an optional scaling factor

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)

Fills the input Tensor with values according to the method described in Understanding the difficulty of training deep feedforward neural networks - Glorot, X. & Bengio, Y. (2010), using a normal distribution. 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 – an n-dimensional torch.Tensor

• gain – an optional scaling factor

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')

Fills the input Tensor with values according to the method described in Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification - He, K. et al. (2015), using a uniform distribution. 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 – an n-dimensional torch.Tensor

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

• mode – 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 – the non-linear function (nn.functional name), recommended to use only with 'relu' or 'leaky_relu' (default).

Examples

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

torch.nn.init.kaiming_normal_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu')

Fills the input Tensor with values according to the method described in Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification - He, K. et al. (2015), using a normal distribution. 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 – an n-dimensional torch.Tensor

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

• mode – 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 – the non-linear function (nn.functional name), recommended to use only with 'relu' or 'leaky_relu' (default).

Examples

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

torch.nn.init.orthogonal_(tensor, gain=1)

Fills the input Tensor with a (semi) orthogonal matrix, as 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 – an n-dimensional torch.Tensor, where $n \geq 2$

• gain – optional scaling factor

Examples

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

torch.nn.init.sparse_(tensor, sparsity, std=0.01)

Fills the 2D input Tensor as a sparse matrix, where 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 – an n-dimensional torch.Tensor

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

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

Examples

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