# Copyright 2022 Cerebras Systems.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
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):
# 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(
f"{mean} is more than 2 std from [{a}, {b}]. "
+ f"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
[docs]def trunc_normal_(tensor, mean=0.0, std=1.0, a=-2.0, b=2.0):
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`.
Args:
tensor (torch.Tensor): an n-dimensional `torch.Tensor`
mean (float): the mean of the normal distribution. Defaults to `0.0`
std (float): the standard deviation of the normal distribution.
Defaults to `1.0`
a (float): the minimum cutoff value. Defaults to `-2.0`
b (float): the maximum cutoff value. Defaults to `2.0`
Examples:
>>> w = torch.empty(3, 3)
>>> trunc_normal_(w)
"""
return _no_grad_trunc_normal_(tensor, mean, std, a, b)
[docs]def variance_scaling_(
tensor, scale=1.0, mode="fan_in", distribution="truncated_normal"
):
r"""Adapted from TensorFlow's initializations
https://www.tensorflow.org/api_docs/python/tf/keras/initializers/VarianceScaling
Fills the input Tensor with values given scale, mode and distribution.
Args:
tensor (torch.Tensor): an n-dimensional `torch.Tensor`
scale (float): scaling factor (positive float)
mode (str): mode of weight initialization. Defaults to `fan_in`
distribution (str): distributino to initialize tensors with. Defaults to
`truncated_normal`
Examples:
>>> w = torch.empty(3, 3)
>>> variance_scaling_(w)
"""
fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
if mode == 'fan_in':
denom = max(1.0, fan_in)
elif mode == 'fan_out':
denom = max(1.0, fan_out)
elif mode == 'fan_avg':
denom = (fan_in + fan_out) / 2
denom = max(1.0, denom)
variance = scale / denom
if distribution == "truncated_normal":
# constant from scipy.stats.truncnorm.std(a=-2, b=2, loc=0., scale=1.)
trunc_normal_(tensor, std=math.sqrt(variance) / 0.87962566103423978)
elif distribution == "normal":
tensor.normal_(std=math.sqrt(variance))
elif distribution == "uniform":
bound = math.sqrt(3 * variance)
tensor.uniform_(-bound, bound)
else:
raise ValueError(f"invalid distribution {distribution}")
[docs]def lecun_normal_(tensor):
r"""Adapted from TensorFlow's initializations
https://www.tensorflow.org/api_docs/python/tf/keras/initializers/LecunNormal
Args:
tensor (torch.Tensor): an n-dimensional `torch.Tensor`
Examples:
>>> w = torch.empty(3, 3)
>>> lecun_normal_(w)
"""
variance_scaling_(tensor, mode="fan_in", distribution="truncated_normal")