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import math
import warnings
import torch
from torch.nn.init import _calculate_fan_in_and_fan_out
def _no_grad_trunc_normal_(tensor, mean, std, a, b):
# Cut & paste from PyTorch official master until it's in a few official releases - RW
# Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
def norm_cdf(x):
# Computes standard normal cumulative distribution function
return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
if (mean < a - 2 * std) or (mean > b + 2 * std):
warnings.warn(
"mean is more than 2 std from [a, b] in nn.init.trunc_normal_. "
"The distribution of values may be incorrect.",
stacklevel=2,
)
with torch.no_grad():
# Values are generated by using a truncated uniform distribution and
# then using the inverse CDF for the normal distribution.
# Get upper and lower cdf values
l = norm_cdf((a - mean) / std)
u = norm_cdf((b - mean) / std)
# Uniformly fill tensor with values from [l, u], then translate to
# [2l-1, 2u-1].
tensor.uniform_(2 * l - 1, 2 * u - 1)
# Use inverse cdf transform for normal distribution to get truncated
# standard normal
tensor.erfinv_()
# Transform to proper mean, std
tensor.mul_(std * math.sqrt(2.0))
tensor.add_(mean)
# Clamp to ensure it's in the proper range
tensor.clamp_(min=a, max=b)
return tensor
def trunc_normal_(
tensor: torch.Tensor, mean=0.0, std=1.0, a=-2.0, b=2.0
) -> torch.Tensor:
r"""Fills the input Tensor with values drawn from a truncated
normal distribution. The values are effectively drawn from the
normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
with values outside :math:`[a, b]` redrawn until they are within
the bounds. The method used for generating the random values works
best when :math:`a \leq \text{mean} \leq b`.
NOTE: this impl is similar to the PyTorch trunc_normal_, the bounds [a, b] are
applied while sampling the normal with mean/std applied, therefore a, b args
should be adjusted to match the range of mean, std args.
Args:
tensor: an n-dimensional `torch.Tensor`
mean: the mean of the normal distribution
std: the standard deviation of the normal distribution
a: the minimum cutoff value
b: the maximum cutoff value
Examples:
>>> w = torch.empty(3, 5)
>>> nn.init.trunc_normal_(w)
"""
return _no_grad_trunc_normal_(tensor, mean, std, a, b)
def trunc_normal_tf_(
tensor: torch.Tensor, mean=0.0, std=1.0, a=-2.0, b=2.0
) -> torch.Tensor:
r"""Fills the input Tensor with values drawn from a truncated
normal distribution. The values are effectively drawn from the
normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^2)`
with values outside :math:`[a, b]` redrawn until they are within
the bounds. The method used for generating the random values works
best when :math:`a \leq \text{mean} \leq b`.
NOTE: this 'tf' variant behaves closer to Tensorflow / JAX impl where the
bounds [a, b] are applied when sampling the normal distribution with mean=0, std=1.0
and the result is subsquently scaled and shifted by the mean and std args.
Args:
tensor: an n-dimensional `torch.Tensor`
mean: the mean of the normal distribution
std: the standard deviation of the normal distribution
a: the minimum cutoff value
b: the maximum cutoff value
Examples:
>>> w = torch.empty(3, 5)
>>> nn.init.trunc_normal_(w)
"""
_no_grad_trunc_normal_(tensor, 0, 1.0, a, b)
with torch.no_grad():
tensor.mul_(std).add_(mean)
return tensor
def variance_scaling_(tensor, scale=1.0, mode="fan_in", distribution="normal"):
fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
if mode == "fan_in":
denom = fan_in
elif mode == "fan_out":
denom = fan_out
elif mode == "fan_avg":
denom = (fan_in + fan_out) / 2
variance = scale / denom # type: ignore
if distribution == "truncated_normal":
# constant is stddev of standard normal truncated to (-2, 2)
trunc_normal_tf_(tensor, std=math.sqrt(variance) / 0.87962566103423978)
elif distribution == "normal":
tensor.normal_(std=math.sqrt(variance))
elif distribution == "uniform":
bound = math.sqrt(3 * variance)
# pylint: disable=invalid-unary-operand-type
tensor.uniform_(-bound, bound)
else:
raise ValueError(f"invalid distribution {distribution}")
def lecun_normal_(tensor):
variance_scaling_(tensor, mode="fan_in", distribution="truncated_normal")
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