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627 lines
21 KiB
627 lines
21 KiB
"""This file contains utilities for initializing neural network parameters."""
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import math
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import warnings
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from torch import Tensor
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import torch
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from typing import Optional as _Optional
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# These no_grad_* functions are necessary as wrappers around the parts of these
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# functions that use `with torch.no_grad()`. The JIT doesn't support context
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# managers, so these need to be implemented as builtins. Using these wrappers
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# lets us keep those builtins small and re-usable.
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def _no_grad_uniform_(tensor, a, b, generator=None):
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with torch.no_grad():
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return tensor.uniform_(a, b, generator=generator)
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def _no_grad_normal_(tensor, mean, std, generator=None):
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with torch.no_grad():
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return tensor.normal_(mean, std, generator=generator)
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def _no_grad_trunc_normal_(tensor, mean, std, a, b, generator=None):
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# Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
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def norm_cdf(x):
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# Computes standard normal cumulative distribution function
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return (1. + math.erf(x / math.sqrt(2.))) / 2.
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if (mean < a - 2 * std) or (mean > b + 2 * std):
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warnings.warn("mean is more than 2 std from [a, b] in nn.init.trunc_normal_. "
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"The distribution of values may be incorrect.",
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stacklevel=2)
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with torch.no_grad():
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# Values are generated by using a truncated uniform distribution and
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# then using the inverse CDF for the normal distribution.
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# Get upper and lower cdf values
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l = norm_cdf((a - mean) / std)
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u = norm_cdf((b - mean) / std)
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# Uniformly fill tensor with values from [l, u], then translate to
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# [2l-1, 2u-1].
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tensor.uniform_(2 * l - 1, 2 * u - 1, generator=generator)
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# Use inverse cdf transform for normal distribution to get truncated
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# standard normal
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tensor.erfinv_()
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# Transform to proper mean, std
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tensor.mul_(std * math.sqrt(2.))
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tensor.add_(mean)
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# Clamp to ensure it's in the proper range
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tensor.clamp_(min=a, max=b)
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return tensor
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def _no_grad_fill_(tensor, val):
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with torch.no_grad():
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return tensor.fill_(val)
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def _no_grad_zero_(tensor):
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with torch.no_grad():
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return tensor.zero_()
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def calculate_gain(nonlinearity, param=None):
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r"""Return the recommended gain value for the given nonlinearity function.
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The values are as follows:
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================= ====================================================
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nonlinearity gain
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================= ====================================================
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Linear / Identity :math:`1`
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Conv{1,2,3}D :math:`1`
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Sigmoid :math:`1`
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Tanh :math:`\frac{5}{3}`
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ReLU :math:`\sqrt{2}`
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Leaky Relu :math:`\sqrt{\frac{2}{1 + \text{negative\_slope}^2}}`
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SELU :math:`\frac{3}{4}`
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================= ====================================================
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.. warning::
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In order to implement `Self-Normalizing Neural Networks`_ ,
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you should use ``nonlinearity='linear'`` instead of ``nonlinearity='selu'``.
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This gives the initial weights a variance of ``1 / N``,
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which is necessary to induce a stable fixed point in the forward pass.
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In contrast, the default gain for ``SELU`` sacrifices the normalization
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effect for more stable gradient flow in rectangular layers.
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Args:
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nonlinearity: the non-linear function (`nn.functional` name)
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param: optional parameter for the non-linear function
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Examples:
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>>> gain = nn.init.calculate_gain('leaky_relu', 0.2) # leaky_relu with negative_slope=0.2
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.. _Self-Normalizing Neural Networks: https://papers.nips.cc/paper/2017/hash/5d44ee6f2c3f71b73125876103c8f6c4-Abstract.html
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"""
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linear_fns = ['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d']
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if nonlinearity in linear_fns or nonlinearity == 'sigmoid':
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return 1
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elif nonlinearity == 'tanh':
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return 5.0 / 3
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elif nonlinearity == 'relu':
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return math.sqrt(2.0)
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elif nonlinearity == 'leaky_relu':
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if param is None:
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negative_slope = 0.01
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elif not isinstance(param, bool) and isinstance(param, int) or isinstance(param, float):
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# True/False are instances of int, hence check above
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negative_slope = param
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else:
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raise ValueError(f"negative_slope {param} not a valid number")
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return math.sqrt(2.0 / (1 + negative_slope ** 2))
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elif nonlinearity == 'selu':
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return 3.0 / 4 # Value found empirically (https://github.com/pytorch/pytorch/pull/50664)
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else:
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raise ValueError(f"Unsupported nonlinearity {nonlinearity}")
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def uniform_(
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tensor: Tensor,
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a: float = 0.0,
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b: float = 1.0,
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generator: _Optional[torch.Generator] = None,
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) -> Tensor:
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r"""Fill the input Tensor with values drawn from the uniform distribution.
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:math:`\mathcal{U}(a, b)`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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a: the lower bound of the uniform distribution
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b: the upper bound of the uniform distribution
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.uniform_(w)
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"""
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if torch.overrides.has_torch_function_variadic(tensor):
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return torch.overrides.handle_torch_function(
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uniform_, (tensor,), tensor=tensor, a=a, b=b, generator=generator
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)
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return _no_grad_uniform_(tensor, a, b, generator)
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def normal_(
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tensor: Tensor,
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mean: float = 0.0,
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std: float = 1.0,
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generator: _Optional[torch.Generator] = None,
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) -> Tensor:
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r"""Fill the input Tensor with values drawn from the normal distribution.
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:math:`\mathcal{N}(\text{mean}, \text{std}^2)`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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mean: the mean of the normal distribution
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std: the standard deviation of the normal distribution
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.normal_(w)
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"""
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if torch.overrides.has_torch_function_variadic(tensor):
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return torch.overrides.handle_torch_function(
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normal_, (tensor,), tensor=tensor, mean=mean, std=std, generator=generator
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)
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return _no_grad_normal_(tensor, mean, std, generator)
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def trunc_normal_(
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tensor: Tensor,
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mean: float = 0.,
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std: float = 1.,
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a: float = -2.,
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b: float = 2.,
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generator: _Optional[torch.Generator] = None
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) -> Tensor:
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r"""Fill the input Tensor with values drawn from a truncated normal distribution.
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The values are effectively drawn from the
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normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
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with values outside :math:`[a, b]` redrawn until they are within
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the bounds. The method used for generating the random values works
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best when :math:`a \leq \text{mean} \leq b`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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mean: the mean of the normal distribution
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std: the standard deviation of the normal distribution
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a: the minimum cutoff value
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b: the maximum cutoff value
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.trunc_normal_(w)
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"""
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return _no_grad_trunc_normal_(tensor, mean, std, a, b, generator=generator)
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def constant_(tensor: Tensor, val: float) -> Tensor:
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r"""Fill the input Tensor with the value :math:`\text{val}`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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val: the value to fill the tensor with
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.constant_(w, 0.3)
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"""
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if torch.overrides.has_torch_function_variadic(tensor):
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return torch.overrides.handle_torch_function(constant_, (tensor,), tensor=tensor, val=val)
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return _no_grad_fill_(tensor, val)
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def ones_(tensor: Tensor) -> Tensor:
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r"""Fill the input Tensor with the scalar value `1`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.ones_(w)
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"""
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return _no_grad_fill_(tensor, 1.)
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def zeros_(tensor: Tensor) -> Tensor:
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r"""Fill the input Tensor with the scalar value `0`.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.zeros_(w)
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"""
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return _no_grad_zero_(tensor)
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def eye_(tensor):
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r"""Fill the 2-dimensional input `Tensor` with the identity matrix.
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Preserves the identity of the inputs in `Linear` layers, where as
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many inputs are preserved as possible.
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Args:
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tensor: a 2-dimensional `torch.Tensor`
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.eye_(w)
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"""
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if tensor.ndimension() != 2:
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raise ValueError("Only tensors with 2 dimensions are supported")
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with torch.no_grad():
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torch.eye(*tensor.shape, out=tensor, requires_grad=tensor.requires_grad)
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return tensor
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def dirac_(tensor, groups=1):
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r"""Fill the {3, 4, 5}-dimensional input `Tensor` with the Dirac delta function.
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Preserves the identity of the inputs in `Convolutional`
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layers, where as many input channels are preserved as possible. In case
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of groups>1, each group of channels preserves identity
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Args:
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tensor: a {3, 4, 5}-dimensional `torch.Tensor`
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groups (int, optional): number of groups in the conv layer (default: 1)
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Examples:
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>>> w = torch.empty(3, 16, 5, 5)
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>>> nn.init.dirac_(w)
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>>> w = torch.empty(3, 24, 5, 5)
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>>> nn.init.dirac_(w, 3)
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"""
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dimensions = tensor.ndimension()
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if dimensions not in [3, 4, 5]:
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raise ValueError("Only tensors with 3, 4, or 5 dimensions are supported")
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sizes = tensor.size()
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if sizes[0] % groups != 0:
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raise ValueError('dim 0 must be divisible by groups')
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out_chans_per_grp = sizes[0] // groups
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min_dim = min(out_chans_per_grp, sizes[1])
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with torch.no_grad():
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tensor.zero_()
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for g in range(groups):
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for d in range(min_dim):
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if dimensions == 3: # Temporal convolution
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tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2] = 1
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elif dimensions == 4: # Spatial convolution
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tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2,
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tensor.size(3) // 2] = 1
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else: # Volumetric convolution
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tensor[g * out_chans_per_grp + d, d, tensor.size(2) // 2,
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tensor.size(3) // 2, tensor.size(4) // 2] = 1
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return tensor
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def _calculate_fan_in_and_fan_out(tensor):
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dimensions = tensor.dim()
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if dimensions < 2:
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raise ValueError("Fan in and fan out can not be computed for tensor with fewer than 2 dimensions")
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num_input_fmaps = tensor.size(1)
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num_output_fmaps = tensor.size(0)
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receptive_field_size = 1
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if tensor.dim() > 2:
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# math.prod is not always available, accumulate the product manually
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# we could use functools.reduce but that is not supported by TorchScript
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for s in tensor.shape[2:]:
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receptive_field_size *= s
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fan_in = num_input_fmaps * receptive_field_size
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fan_out = num_output_fmaps * receptive_field_size
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return fan_in, fan_out
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def xavier_uniform_(
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tensor: Tensor, gain: float = 1.0, generator: _Optional[torch.Generator] = None
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) -> Tensor:
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r"""Fill the input `Tensor` with values using a Xavier uniform distribution.
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The method is described in `Understanding the difficulty of training
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deep feedforward neural networks` - Glorot, X. & Bengio, Y. (2010).
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The resulting tensor will have values sampled from
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:math:`\mathcal{U}(-a, a)` where
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.. math::
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a = \text{gain} \times \sqrt{\frac{6}{\text{fan\_in} + \text{fan\_out}}}
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Also known as Glorot initialization.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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gain: an optional scaling factor
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain('relu'))
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"""
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fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
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std = gain * math.sqrt(2.0 / float(fan_in + fan_out))
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a = math.sqrt(3.0) * std # Calculate uniform bounds from standard deviation
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return _no_grad_uniform_(tensor, -a, a, generator)
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def xavier_normal_(
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tensor: Tensor,
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gain: float = 1.0,
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generator: _Optional[torch.Generator] = None,
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) -> Tensor:
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r"""Fill the input `Tensor` with values using a Xavier normal distribution.
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The method is described in `Understanding the difficulty of training deep feedforward
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neural networks` - Glorot, X. & Bengio, Y. (2010). The resulting tensor
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will have values sampled from :math:`\mathcal{N}(0, \text{std}^2)` where
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.. math::
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\text{std} = \text{gain} \times \sqrt{\frac{2}{\text{fan\_in} + \text{fan\_out}}}
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Also known as Glorot initialization.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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gain: an optional scaling factor
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.xavier_normal_(w)
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"""
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fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
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std = gain * math.sqrt(2.0 / float(fan_in + fan_out))
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return _no_grad_normal_(tensor, 0., std, generator)
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def _calculate_correct_fan(tensor, mode):
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mode = mode.lower()
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valid_modes = ['fan_in', 'fan_out']
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if mode not in valid_modes:
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raise ValueError(f"Mode {mode} not supported, please use one of {valid_modes}")
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fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
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return fan_in if mode == 'fan_in' else fan_out
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def kaiming_uniform_(
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tensor: Tensor,
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a: float = 0,
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mode: str = "fan_in",
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nonlinearity: str = "leaky_relu",
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generator: _Optional[torch.Generator] = None,
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):
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r"""Fill the input `Tensor` with values using a Kaiming uniform distribution.
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The method is described in `Delving deep into rectifiers: Surpassing
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human-level performance on ImageNet classification` - He, K. et al. (2015).
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The resulting tensor will have values sampled from
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:math:`\mathcal{U}(-\text{bound}, \text{bound})` where
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.. math::
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\text{bound} = \text{gain} \times \sqrt{\frac{3}{\text{fan\_mode}}}
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Also known as He initialization.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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a: the negative slope of the rectifier used after this layer (only
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used with ``'leaky_relu'``)
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mode: either ``'fan_in'`` (default) or ``'fan_out'``. Choosing ``'fan_in'``
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preserves the magnitude of the variance of the weights in the
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forward pass. Choosing ``'fan_out'`` preserves the magnitudes in the
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backwards pass.
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nonlinearity: the non-linear function (`nn.functional` name),
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recommended to use only with ``'relu'`` or ``'leaky_relu'`` (default).
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generator: the torch Generator to sample from (default: None)
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Examples:
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>>> w = torch.empty(3, 5)
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>>> nn.init.kaiming_uniform_(w, mode='fan_in', nonlinearity='relu')
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"""
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if torch.overrides.has_torch_function_variadic(tensor):
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return torch.overrides.handle_torch_function(
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kaiming_uniform_,
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(tensor,),
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tensor=tensor,
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a=a,
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mode=mode,
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nonlinearity=nonlinearity,
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generator=generator)
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if 0 in tensor.shape:
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warnings.warn("Initializing zero-element tensors is a no-op")
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return tensor
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fan = _calculate_correct_fan(tensor, mode)
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gain = calculate_gain(nonlinearity, a)
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std = gain / math.sqrt(fan)
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bound = math.sqrt(3.0) * std # Calculate uniform bounds from standard deviation
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with torch.no_grad():
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return tensor.uniform_(-bound, bound, generator=generator)
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def kaiming_normal_(
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tensor: Tensor,
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a: float = 0,
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mode: str = "fan_in",
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nonlinearity: str = "leaky_relu",
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generator: _Optional[torch.Generator] = None,
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):
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r"""Fill the input `Tensor` with values using a Kaiming normal distribution.
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The method is described in `Delving deep into rectifiers: Surpassing
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human-level performance on ImageNet classification` - He, K. et al. (2015).
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The resulting tensor will have values sampled from
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:math:`\mathcal{N}(0, \text{std}^2)` where
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.. math::
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\text{std} = \frac{\text{gain}}{\sqrt{\text{fan\_mode}}}
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Also known as He initialization.
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Args:
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tensor: an n-dimensional `torch.Tensor`
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a: the negative slope of the rectifier used after this layer (only
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used with ``'leaky_relu'``)
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mode: either ``'fan_in'`` (default) or ``'fan_out'``. Choosing ``'fan_in'``
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|
preserves the magnitude of the variance of the weights in the
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forward pass. Choosing ``'fan_out'`` preserves the magnitudes in the
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backwards pass.
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nonlinearity: the non-linear function (`nn.functional` name),
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recommended to use only with ``'relu'`` or ``'leaky_relu'`` (default).
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generator: the torch Generator to sample from (default: None)
|
|
|
|
Examples:
|
|
>>> w = torch.empty(3, 5)
|
|
>>> nn.init.kaiming_normal_(w, mode='fan_out', nonlinearity='relu')
|
|
"""
|
|
if 0 in tensor.shape:
|
|
warnings.warn("Initializing zero-element tensors is a no-op")
|
|
return tensor
|
|
fan = _calculate_correct_fan(tensor, mode)
|
|
gain = calculate_gain(nonlinearity, a)
|
|
std = gain / math.sqrt(fan)
|
|
with torch.no_grad():
|
|
return tensor.normal_(0, std, generator=generator)
|
|
|
|
|
|
def orthogonal_(
|
|
tensor,
|
|
gain=1,
|
|
generator: _Optional[torch.Generator] = None,
|
|
):
|
|
r"""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.
|
|
|
|
Args:
|
|
tensor: an n-dimensional `torch.Tensor`, where :math:`n \geq 2`
|
|
gain: optional scaling factor
|
|
generator: the torch Generator to sample from (default: None)
|
|
|
|
Examples:
|
|
>>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_LAPACK)
|
|
>>> w = torch.empty(3, 5)
|
|
>>> nn.init.orthogonal_(w)
|
|
"""
|
|
if tensor.ndimension() < 2:
|
|
raise ValueError("Only tensors with 2 or more dimensions are supported")
|
|
|
|
if tensor.numel() == 0:
|
|
# no-op
|
|
return tensor
|
|
rows = tensor.size(0)
|
|
cols = tensor.numel() // rows
|
|
flattened = tensor.new(rows, cols).normal_(0, 1, generator=generator)
|
|
|
|
if rows < cols:
|
|
flattened.t_()
|
|
|
|
# Compute the qr factorization
|
|
q, r = torch.linalg.qr(flattened)
|
|
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
|
|
d = torch.diag(r, 0)
|
|
ph = d.sign()
|
|
q *= ph
|
|
|
|
if rows < cols:
|
|
q.t_()
|
|
|
|
with torch.no_grad():
|
|
tensor.view_as(q).copy_(q)
|
|
tensor.mul_(gain)
|
|
return tensor
|
|
|
|
|
|
def sparse_(
|
|
tensor,
|
|
sparsity,
|
|
std=0.01,
|
|
generator: _Optional[torch.Generator] = None,
|
|
):
|
|
r"""Fill the 2D input `Tensor` as a sparse matrix.
|
|
|
|
The non-zero elements will be drawn from the normal distribution
|
|
:math:`\mathcal{N}(0, 0.01)`, as described in `Deep learning via
|
|
Hessian-free optimization` - Martens, J. (2010).
|
|
|
|
Args:
|
|
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
|
|
generator: the torch Generator to sample from (default: None)
|
|
|
|
Examples:
|
|
>>> w = torch.empty(3, 5)
|
|
>>> nn.init.sparse_(w, sparsity=0.1)
|
|
"""
|
|
if tensor.ndimension() != 2:
|
|
raise ValueError("Only tensors with 2 dimensions are supported")
|
|
|
|
rows, cols = tensor.shape
|
|
num_zeros = int(math.ceil(sparsity * rows))
|
|
|
|
with torch.no_grad():
|
|
tensor.normal_(0, std, generator=generator)
|
|
for col_idx in range(cols):
|
|
row_indices = torch.randperm(rows)
|
|
zero_indices = row_indices[:num_zeros]
|
|
tensor[zero_indices, col_idx] = 0
|
|
return tensor
|
|
|
|
|
|
# for backward compatibility
|
|
def _make_deprecate(meth):
|
|
new_name = meth.__name__
|
|
old_name = new_name[:-1]
|
|
|
|
def deprecated_init(*args, **kwargs):
|
|
warnings.warn(f"nn.init.{old_name} is now deprecated in favor of nn.init.{new_name}.", stacklevel=2)
|
|
return meth(*args, **kwargs)
|
|
|
|
deprecated_init.__doc__ = fr"""
|
|
{old_name}(...)
|
|
|
|
.. warning::
|
|
This method is now deprecated in favor of :func:`torch.nn.init.{new_name}`.
|
|
|
|
See :func:`~torch.nn.init.{new_name}` for details."""
|
|
deprecated_init.__name__ = old_name
|
|
return deprecated_init
|
|
|
|
|
|
uniform = _make_deprecate(uniform_)
|
|
normal = _make_deprecate(normal_)
|
|
constant = _make_deprecate(constant_)
|
|
eye = _make_deprecate(eye_)
|
|
dirac = _make_deprecate(dirac_)
|
|
xavier_uniform = _make_deprecate(xavier_uniform_)
|
|
xavier_normal = _make_deprecate(xavier_normal_)
|
|
kaiming_uniform = _make_deprecate(kaiming_uniform_)
|
|
kaiming_normal = _make_deprecate(kaiming_normal_)
|
|
orthogonal = _make_deprecate(orthogonal_)
|
|
sparse = _make_deprecate(sparse_)
|