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# cp from https://github.com/lifeiteng/vall-e/blob/main/valle/modules/scaling.py | |
# Copyright 2022 Xiaomi Corp. (authors: Daniel Povey) | |
# | |
# See ../../../../LICENSE for clarification regarding multiple authors | |
# | |
# 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 collections | |
import logging | |
import random | |
import math | |
from functools import reduce | |
from itertools import repeat | |
from typing import Optional, Tuple, Union | |
import torch | |
import torch.nn as nn | |
import torch.nn.functional as F | |
from torch import Tensor | |
from torch.nn import Embedding as ScaledEmbedding | |
# from valle.utils import Transpose | |
class Transpose(nn.Identity): | |
"""(N, T, D) -> (N, D, T)""" | |
def forward(self, input: torch.Tensor) -> torch.Tensor: | |
return input.transpose(1, 2) | |
class ActivationBalancerFunction(torch.autograd.Function): | |
def forward( | |
ctx, | |
x: Tensor, | |
scale_factor: Tensor, | |
sign_factor: Optional[Tensor], | |
channel_dim: int, | |
) -> Tensor: | |
if channel_dim < 0: | |
channel_dim += x.ndim | |
ctx.channel_dim = channel_dim | |
xgt0 = x > 0 | |
if sign_factor is None: | |
ctx.save_for_backward(xgt0, scale_factor) | |
else: | |
ctx.save_for_backward(xgt0, scale_factor, sign_factor) | |
return x | |
def backward(ctx, x_grad: Tensor) -> Tuple[Tensor, None, None, None]: | |
if len(ctx.saved_tensors) == 3: | |
xgt0, scale_factor, sign_factor = ctx.saved_tensors | |
for _ in range(ctx.channel_dim, x_grad.ndim - 1): | |
scale_factor = scale_factor.unsqueeze(-1) | |
sign_factor = sign_factor.unsqueeze(-1) | |
factor = sign_factor + scale_factor * (xgt0.to(x_grad.dtype) - 0.5) | |
else: | |
xgt0, scale_factor = ctx.saved_tensors | |
for _ in range(ctx.channel_dim, x_grad.ndim - 1): | |
scale_factor = scale_factor.unsqueeze(-1) | |
factor = scale_factor * (xgt0.to(x_grad.dtype) - 0.5) | |
neg_delta_grad = x_grad.abs() * factor | |
return ( | |
x_grad - neg_delta_grad, | |
None, | |
None, | |
None, | |
) | |
def _compute_scale_factor( | |
x: Tensor, | |
channel_dim: int, | |
min_abs: float, | |
max_abs: float, | |
gain_factor: float, | |
max_factor: float, | |
) -> Tensor: | |
if channel_dim < 0: | |
channel_dim += x.ndim | |
sum_dims = [d for d in range(x.ndim) if d != channel_dim] | |
x_abs_mean = torch.mean(x.abs(), dim=sum_dims).to(torch.float32) | |
if min_abs == 0.0: | |
below_threshold = 0.0 | |
else: | |
# below_threshold is 0 if x_abs_mean > min_abs, can be at most max_factor if | |
# x_abs)_mean , min_abs. | |
below_threshold = ( | |
(min_abs - x_abs_mean) * (gain_factor / min_abs) | |
).clamp(min=0, max=max_factor) | |
above_threshold = ((x_abs_mean - max_abs) * (gain_factor / max_abs)).clamp( | |
min=0, max=max_factor | |
) | |
return below_threshold - above_threshold | |
def _compute_sign_factor( | |
x: Tensor, | |
channel_dim: int, | |
min_positive: float, | |
max_positive: float, | |
gain_factor: float, | |
max_factor: float, | |
) -> Tensor: | |
if channel_dim < 0: | |
channel_dim += x.ndim | |
sum_dims = [d for d in range(x.ndim) if d != channel_dim] | |
proportion_positive = torch.mean((x > 0).to(torch.float32), dim=sum_dims) | |
if min_positive == 0.0: | |
factor1 = 0.0 | |
else: | |
# 0 if proportion_positive >= min_positive, else can be | |
# as large as max_factor. | |
factor1 = ( | |
(min_positive - proportion_positive) * (gain_factor / min_positive) | |
).clamp_(min=0, max=max_factor) | |
if max_positive == 1.0: | |
factor2 = 0.0 | |
else: | |
# 0 if self.proportion_positive <= max_positive, else can be | |
# as large as -max_factor. | |
factor2 = ( | |
(proportion_positive - max_positive) | |
* (gain_factor / (1.0 - max_positive)) | |
).clamp_(min=0, max=max_factor) | |
sign_factor = factor1 - factor2 | |
# require min_positive != 0 or max_positive != 1: | |
assert not isinstance(sign_factor, float) | |
return sign_factor | |
class ActivationScaleBalancerFunction(torch.autograd.Function): | |
""" | |
This object is used in class ActivationBalancer when the user specified | |
min_positive=0, max_positive=1, so there are no constraints on the signs | |
of the activations and only the absolute value has a constraint. | |
""" | |
def forward( | |
ctx, | |
x: Tensor, | |
sign_factor: Tensor, | |
scale_factor: Tensor, | |
channel_dim: int, | |
) -> Tensor: | |
if channel_dim < 0: | |
channel_dim += x.ndim | |
ctx.channel_dim = channel_dim | |
xgt0 = x > 0 | |
ctx.save_for_backward(xgt0, sign_factor, scale_factor) | |
return x | |
def backward(ctx, x_grad: Tensor) -> Tuple[Tensor, None, None, None]: | |
xgt0, sign_factor, scale_factor = ctx.saved_tensors | |
for _ in range(ctx.channel_dim, x_grad.ndim - 1): | |
sign_factor = sign_factor.unsqueeze(-1) | |
scale_factor = scale_factor.unsqueeze(-1) | |
factor = sign_factor + scale_factor * (xgt0.to(x_grad.dtype) - 0.5) | |
neg_delta_grad = x_grad.abs() * factor | |
return ( | |
x_grad - neg_delta_grad, | |
None, | |
None, | |
None, | |
) | |
class RandomClampFunction(torch.autograd.Function): | |
def forward( | |
ctx, | |
x: Tensor, | |
min: Optional[float], | |
max: Optional[float], | |
prob: float, | |
reflect: float, | |
) -> Tensor: | |
x_clamped = torch.clamp(x, min=min, max=max) | |
mask = torch.rand_like(x) < prob | |
ans = torch.where(mask, x_clamped, x) | |
if x.requires_grad: | |
ctx.save_for_backward(ans == x) | |
ctx.reflect = reflect | |
if reflect != 0.0: | |
ans = ans * (1.0 + reflect) - (x * reflect) | |
return ans | |
def backward( | |
ctx, ans_grad: Tensor | |
) -> Tuple[Tensor, None, None, None, None]: | |
(is_same,) = ctx.saved_tensors | |
x_grad = ans_grad * is_same.to(ans_grad.dtype) | |
reflect = ctx.reflect | |
if reflect != 0.0: | |
x_grad = x_grad * (1.0 + reflect) - (ans_grad * reflect) | |
return x_grad, None, None, None, None | |
def random_clamp( | |
x: Tensor, | |
min: Optional[float] = None, | |
max: Optional[float] = None, | |
prob: float = 0.5, | |
reflect: float = 0.0, | |
): | |
return RandomClampFunction.apply(x, min, max, prob, reflect) | |
def random_cast_to_half(x: Tensor, min_abs: float = 5.0e-06) -> Tensor: | |
""" | |
A randomized way of casting a floating point value to half precision. | |
""" | |
if x.dtype == torch.float16: | |
return x | |
x_abs = x.abs() | |
is_too_small = x_abs < min_abs | |
# for elements where is_too_small is true, random_val will contain +-min_abs with | |
# probability (x.abs() / min_abs), and 0.0 otherwise. [so this preserves expectations, | |
# for those elements]. | |
random_val = min_abs * x.sign() * (torch.rand_like(x) * min_abs < x_abs) | |
return torch.where(is_too_small, random_val, x).to(torch.float16) | |
class RandomGradFunction(torch.autograd.Function): | |
""" | |
Does nothing in forward pass; in backward pass, gets rid of very small grads using | |
randomized approach that preserves expectations (intended to reduce roundoff). | |
""" | |
def forward(ctx, x: Tensor, min_abs: float) -> Tensor: | |
ctx.min_abs = min_abs | |
return x | |
def backward(ctx, ans_grad: Tensor) -> Tuple[Tensor, None]: | |
if ans_grad.dtype == torch.float16: | |
return ( | |
random_cast_to_half( | |
ans_grad.to(torch.float32), min_abs=ctx.min_abs | |
), | |
None, | |
) | |
else: | |
return ans_grad, None | |
class RandomGrad(torch.nn.Module): | |
""" | |
Gets rid of very small gradients using an expectation-preserving method, intended to increase | |
accuracy of training when using amp (automatic mixed precision) | |
""" | |
def __init__(self, min_abs: float = 5.0e-06): | |
super(RandomGrad, self).__init__() | |
self.min_abs = min_abs | |
def forward(self, x: Tensor): | |
if ( | |
torch.jit.is_scripting() | |
or not self.training | |
or torch.jit.is_tracing() | |
): | |
return x | |
else: | |
return RandomGradFunction.apply(x, self.min_abs) | |
class SoftmaxFunction(torch.autograd.Function): | |
""" | |
Tries to handle half-precision derivatives in a randomized way that should | |
be more accurate for training than the default behavior. | |
""" | |
def forward(ctx, x: Tensor, dim: int): | |
ans = x.softmax(dim=dim) | |
# if x dtype is float16, x.softmax() returns a float32 because | |
# (presumably) that op does not support float16, and autocast | |
# is enabled. | |
if torch.is_autocast_enabled(): | |
ans = ans.to(torch.float16) | |
ctx.save_for_backward(ans) | |
ctx.x_dtype = x.dtype | |
ctx.dim = dim | |
return ans | |
def backward(ctx, ans_grad: Tensor): | |
(ans,) = ctx.saved_tensors | |
with torch.cuda.amp.autocast(enabled=False): | |
ans_grad = ans_grad.to(torch.float32) | |
ans = ans.to(torch.float32) | |
x_grad = ans_grad * ans | |
x_grad = x_grad - ans * x_grad.sum(dim=ctx.dim, keepdim=True) | |
return x_grad, None | |
def softmax(x: Tensor, dim: int): | |
if torch.jit.is_scripting() or torch.jit.is_tracing(): | |
return x.softmax(dim) | |
return SoftmaxFunction.apply(x, dim) | |
class MaxEigLimiterFunction(torch.autograd.Function): | |
def forward( | |
ctx, | |
x: Tensor, | |
coeffs: Tensor, | |
direction: Tensor, | |
channel_dim: int, | |
grad_scale: float, | |
) -> Tensor: | |
ctx.channel_dim = channel_dim | |
ctx.grad_scale = grad_scale | |
ctx.save_for_backward(x.detach(), coeffs.detach(), direction.detach()) | |
return x | |
def backward(ctx, x_grad, *args): | |
with torch.enable_grad(): | |
(x_orig, coeffs, new_direction) = ctx.saved_tensors | |
x_orig.requires_grad = True | |
num_channels = x_orig.shape[ctx.channel_dim] | |
x = x_orig.transpose(ctx.channel_dim, -1).reshape(-1, num_channels) | |
new_direction.requires_grad = False | |
x = x - x.mean(dim=0) | |
x_var = (x ** 2).mean() | |
x_residual = x - coeffs * new_direction | |
x_residual_var = (x_residual ** 2).mean() | |
# `variance_proportion` is the proportion of the variance accounted for | |
# by the top eigen-direction. This is to be minimized. | |
variance_proportion = (x_var - x_residual_var) / (x_var + 1.0e-20) | |
variance_proportion.backward() | |
x_orig_grad = x_orig.grad | |
x_extra_grad = ( | |
x_orig.grad | |
* ctx.grad_scale | |
* x_grad.norm() | |
/ (x_orig_grad.norm() + 1.0e-20) | |
) | |
return x_grad + x_extra_grad.detach(), None, None, None, None | |
class BasicNorm(torch.nn.Module): | |
""" | |
This is intended to be a simpler, and hopefully cheaper, replacement for | |
LayerNorm. The observation this is based on, is that Transformer-type | |
networks, especially with pre-norm, sometimes seem to set one of the | |
feature dimensions to a large constant value (e.g. 50), which "defeats" | |
the LayerNorm because the output magnitude is then not strongly dependent | |
on the other (useful) features. Presumably the weight and bias of the | |
LayerNorm are required to allow it to do this. | |
So the idea is to introduce this large constant value as an explicit | |
parameter, that takes the role of the "eps" in LayerNorm, so the network | |
doesn't have to do this trick. We make the "eps" learnable. | |
Args: | |
num_channels: the number of channels, e.g. 512. | |
channel_dim: the axis/dimension corresponding to the channel, | |
interprted as an offset from the input's ndim if negative. | |
shis is NOT the num_channels; it should typically be one of | |
{-2, -1, 0, 1, 2, 3}. | |
eps: the initial "epsilon" that we add as ballast in: | |
scale = ((input_vec**2).mean() + epsilon)**-0.5 | |
Note: our epsilon is actually large, but we keep the name | |
to indicate the connection with conventional LayerNorm. | |
learn_eps: if true, we learn epsilon; if false, we keep it | |
at the initial value. | |
eps_min: float | |
eps_max: float | |
""" | |
def __init__( | |
self, | |
num_channels: int, | |
channel_dim: int = -1, # CAUTION: see documentation. | |
eps: float = 0.25, | |
learn_eps: bool = True, | |
eps_min: float = -3.0, | |
eps_max: float = 3.0, | |
) -> None: | |
super(BasicNorm, self).__init__() | |
self.num_channels = num_channels | |
self.channel_dim = channel_dim | |
if learn_eps: | |
self.eps = nn.Parameter(torch.tensor(eps).log().detach()) | |
else: | |
self.register_buffer("eps", torch.tensor(eps).log().detach()) | |
self.eps_min = eps_min | |
self.eps_max = eps_max | |
def forward(self, x: Tensor) -> Tensor: | |
assert x.shape[self.channel_dim] == self.num_channels | |
eps = self.eps | |
if self.training and random.random() < 0.25: | |
# with probability 0.25, in training mode, clamp eps between the min | |
# and max; this will encourage it to learn parameters within the | |
# allowed range by making parameters that are outside the allowed | |
# range noisy. | |
# gradients to allow the parameter to get back into the allowed region if it happens to exit it. | |
eps = eps.clamp(min=self.eps_min, max=self.eps_max) | |
scales = ( | |
torch.mean(x ** 2, dim=self.channel_dim, keepdim=True) + eps.exp() | |
) ** -0.5 | |
return x * scales | |
def ScaledLinear(*args, initial_scale: float = 1.0, **kwargs) -> nn.Linear: | |
""" | |
Behaves like a constructor of a modified version of nn.Linear | |
that gives an easy way to set the default initial parameter scale. | |
Args: | |
Accepts the standard args and kwargs that nn.Linear accepts | |
e.g. in_features, out_features, bias=False. | |
initial_scale: you can override this if you want to increase | |
or decrease the initial magnitude of the module's output | |
(affects the initialization of weight_scale and bias_scale). | |
Another option, if you want to do something like this, is | |
to re-initialize the parameters. | |
""" | |
ans = nn.Linear(*args, **kwargs) | |
with torch.no_grad(): | |
ans.weight[:] *= initial_scale | |
if ans.bias is not None: | |
torch.nn.init.uniform_( | |
ans.bias, -0.1 * initial_scale, 0.1 * initial_scale | |
) | |
return ans | |
def ScaledConv1d( | |
*args, | |
initial_scale: float = 1.0, | |
kernel_size: int = 3, | |
padding: str = "same", | |
**kwargs, | |
) -> nn.Conv1d: | |
""" | |
Behaves like a constructor of a modified version of nn.Conv1d | |
that gives an easy way to set the default initial parameter scale. | |
Args: | |
Accepts the standard args and kwargs that nn.Linear accepts | |
e.g. in_features, out_features, bias=False. | |
initial_scale: you can override this if you want to increase | |
or decrease the initial magnitude of the module's output | |
(affects the initialization of weight_scale and bias_scale). | |
Another option, if you want to do something like this, is | |
to re-initialize the parameters. | |
""" | |
ans = nn.Conv1d(*args, kernel_size=kernel_size, padding=padding, **kwargs) | |
with torch.no_grad(): | |
ans.weight[:] *= initial_scale | |
if ans.bias is not None: | |
torch.nn.init.uniform_( | |
ans.bias, -0.1 * initial_scale, 0.1 * initial_scale | |
) | |
return ans | |
def TransposeScaledConv1d( | |
*args, | |
initial_scale: float = 1.0, | |
kernel_size: int = 3, | |
padding: str = "same", | |
**kwargs, | |
) -> nn.Sequential: | |
""" | |
Transpose -> ScaledConv1d | |
""" | |
return nn.Sequential( | |
Transpose(), | |
ScaledConv1d( | |
*args, | |
initial_scale=initial_scale, | |
kernel_size=kernel_size, | |
padding=padding, | |
**kwargs, | |
), | |
) | |
def ScaledConv1dTranspose( | |
*args, | |
initial_scale: float = 1.0, | |
kernel_size: int = 3, | |
padding: str = "same", | |
**kwargs, | |
) -> nn.Sequential: | |
""" | |
Transpose -> ScaledConv1d | |
""" | |
return nn.Sequential( | |
ScaledConv1d( | |
*args, | |
initial_scale=initial_scale, | |
kernel_size=kernel_size, | |
padding=padding, | |
**kwargs, | |
), | |
Transpose(), | |
) | |
def TransposeConv1d( | |
*args, kernel_size: int = 3, padding: str = "same", **kwargs | |
) -> nn.Sequential: | |
""" | |
Transpose -> Conv1d | |
""" | |
return nn.Sequential( | |
Transpose(), | |
nn.Conv1d(*args, kernel_size=kernel_size, padding=padding, **kwargs), | |
) | |
def Conv1dTranspose( | |
*args, kernel_size: int = 3, padding: str = "same", **kwargs | |
) -> nn.Sequential: | |
""" | |
ScaledConv1d -> Transpose | |
""" | |
return nn.Sequential( | |
nn.Conv1d(*args, kernel_size=kernel_size, padding=padding, **kwargs), | |
Transpose(), | |
) | |
class SRLinear(nn.Linear): | |
"""https://arxiv.org/abs/2303.06296 | |
Stabilizing Transformer Training by Preventing Attention Entropy Collapse | |
""" | |
def __init__(self, in_features, out_features, bias=True, **kwargs): | |
super().__init__(in_features, out_features, bias=bias, **kwargs) | |
self.register_buffer( | |
"u", nn.functional.normalize(torch.randn(in_features), dim=0) | |
) | |
with torch.no_grad(): | |
sigma = self.get_sigma() | |
self.register_buffer("spectral_norm", sigma) | |
self.sigma = nn.Parameter(torch.ones(1)) | |
def get_sigma(self): | |
with torch.no_grad(): | |
u = self.u | |
v = self.weight.mv(u) | |
v = nn.functional.normalize(v, dim=0) | |
u = self.weight.T.mv(v) | |
u = nn.functional.normalize(u, dim=0) | |
self.u.data.copy_(u) | |
return torch.einsum("c,cd,d->", v, self.weight, u) | |
def get_weight(self): | |
sigma = self.get_sigma() | |
if self.training: | |
self.spectral_norm.data.copy_(sigma) | |
weight = (self.sigma / sigma) * self.weight | |
return weight | |
def forward(self, x): | |
return nn.functional.linear(x, self.get_weight(), self.bias) | |
class SRConv1d(SRLinear): | |
def __init__( | |
self, | |
in_features, | |
out_features, | |
kernel_size, | |
stride: int = 1, | |
padding: str = "same", | |
bias: bool = True, | |
**kwargs, | |
): | |
in_features = in_features * kernel_size | |
super().__init__(in_features, out_features, bias=bias, **kwargs) | |
nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5)) | |
self.kernel_size = kernel_size | |
self.stride = stride | |
self.padding = padding | |
def forward(self, x): | |
in_features = self.in_features // self.kernel_size | |
weight = self.get_weight().view( | |
self.out_features, in_features, self.kernel_size | |
) | |
return nn.functional.conv1d( | |
x, weight, bias=self.bias, stride=self.stride, padding=self.padding | |
) | |
def TransposeSRConv1d( | |
*args, kernel_size: int = 3, padding: str = "same", **kwargs | |
) -> nn.Sequential: | |
""" | |
Transpose -> SRConv1d | |
""" | |
return nn.Sequential( | |
Transpose(), | |
SRConv1d(*args, kernel_size=kernel_size, padding=padding, **kwargs), | |
) | |
def SRConv1dTranspose( | |
*args, kernel_size: int = 3, padding: str = "same", **kwargs | |
) -> nn.Sequential: | |
""" | |
SRConv1d -> Transpose | |
""" | |
return nn.Sequential( | |
SRConv1d(*args, kernel_size=kernel_size, padding=padding, **kwargs), | |
Transpose(), | |
) | |
class ActivationBalancer(torch.nn.Module): | |
""" | |
Modifies the backpropped derivatives of a function to try to encourage, for | |
each channel, that it is positive at least a proportion `threshold` of the | |
time. It does this by multiplying negative derivative values by up to | |
(1+max_factor), and positive derivative values by up to (1-max_factor), | |
interpolated from 1 at the threshold to those extremal values when none | |
of the inputs are positive. | |
Args: | |
num_channels: the number of channels | |
channel_dim: the dimension/axis corresponding to the channel, e.g. | |
-1, 0, 1, 2; will be interpreted as an offset from x.ndim if negative. | |
min_positive: the minimum, per channel, of the proportion of the time | |
that (x > 0), below which we start to modify the derivatives. | |
max_positive: the maximum, per channel, of the proportion of the time | |
that (x > 0), above which we start to modify the derivatives. | |
max_factor: the maximum factor by which we modify the derivatives for | |
either the sign constraint or the magnitude constraint; | |
e.g. with max_factor=0.02, the the derivatives would be multiplied by | |
values in the range [0.98..1.02]. | |
sign_gain_factor: determines the 'gain' with which we increase the | |
change in gradient once the constraints on min_positive and max_positive | |
are violated. | |
scale_gain_factor: determines the 'gain' with which we increase the | |
change in gradient once the constraints on min_abs and max_abs | |
are violated. | |
min_abs: the minimum average-absolute-value difference from the mean | |
value per channel, which we allow, before we start to modify | |
the derivatives to prevent this. | |
max_abs: the maximum average-absolute-value difference from the mean | |
value per channel, which we allow, before we start to modify | |
the derivatives to prevent this. | |
min_prob: determines the minimum probability with which we modify the | |
gradients for the {min,max}_positive and {min,max}_abs constraints, | |
on each forward(). This is done randomly to prevent all layers | |
from doing it at the same time. Early in training we may use | |
higher probabilities than this; it will decay to this value. | |
""" | |
def __init__( | |
self, | |
num_channels: int, | |
channel_dim: int, | |
min_positive: float = 0.05, | |
max_positive: float = 0.95, | |
max_factor: float = 0.04, | |
sign_gain_factor: float = 0.01, | |
scale_gain_factor: float = 0.02, | |
min_abs: float = 0.2, | |
max_abs: float = 100.0, | |
min_prob: float = 0.1, | |
): | |
super(ActivationBalancer, self).__init__() | |
self.num_channels = num_channels | |
self.channel_dim = channel_dim | |
self.min_positive = min_positive | |
self.max_positive = max_positive | |
self.max_factor = max_factor | |
self.min_abs = min_abs | |
self.max_abs = max_abs | |
self.min_prob = min_prob | |
self.sign_gain_factor = sign_gain_factor | |
self.scale_gain_factor = scale_gain_factor | |
# count measures how many times the forward() function has been called. | |
# We occasionally sync this to a tensor called `count`, that exists to | |
# make sure it is synced to disk when we load and save the model. | |
self.cpu_count = 0 | |
self.register_buffer("count", torch.tensor(0, dtype=torch.int64)) | |
def forward(self, x: Tensor) -> Tensor: | |
if ( | |
torch.jit.is_scripting() | |
or not x.requires_grad | |
or torch.jit.is_tracing() | |
): | |
return _no_op(x) | |
count = self.cpu_count | |
self.cpu_count += 1 | |
if random.random() < 0.01: | |
# Occasionally sync self.cpu_count with self.count. | |
# count affects the decay of 'prob'. don't do this on every iter, | |
# because syncing with the GPU is slow. | |
self.cpu_count = max(self.cpu_count, self.count.item()) | |
self.count.fill_(self.cpu_count) | |
# the prob of doing some work exponentially decreases from 0.5 till it hits | |
# a floor at min_prob (==0.1, by default) | |
prob = max(self.min_prob, 0.5 ** (1 + (count / 4000.0))) | |
if random.random() < prob: | |
sign_gain_factor = 0.5 | |
if self.min_positive != 0.0 or self.max_positive != 1.0: | |
sign_factor = _compute_sign_factor( | |
x, | |
self.channel_dim, | |
self.min_positive, | |
self.max_positive, | |
gain_factor=self.sign_gain_factor / prob, | |
max_factor=self.max_factor, | |
) | |
else: | |
sign_factor = None | |
scale_factor = _compute_scale_factor( | |
x.detach(), | |
self.channel_dim, | |
min_abs=self.min_abs, | |
max_abs=self.max_abs, | |
gain_factor=self.scale_gain_factor / prob, | |
max_factor=self.max_factor, | |
) | |
return ActivationBalancerFunction.apply( | |
x, | |
scale_factor, | |
sign_factor, | |
self.channel_dim, | |
) | |
else: | |
return _no_op(x) | |
def penalize_abs_values_gt(x: Tensor, limit: float, penalty: float) -> Tensor: | |
""" | |
Returns x unmodified, but in backprop will put a penalty for the excess of | |
the absolute values of elements of x over the limit "limit". E.g. if | |
limit == 10.0, then if x has any values over 10 it will get a penalty. | |
Caution: the value of this penalty will be affected by grad scaling used | |
in automatic mixed precision training. For this reasons we use this, | |
it shouldn't really matter, or may even be helpful; we just use this | |
to disallow really implausible values of scores to be given to softmax. | |
""" | |
x_sign = x.sign() | |
over_limit = (x.abs() - limit) > 0 | |
# The following is a memory efficient way to penalize the absolute values of | |
# x that's over the limit. (The memory efficiency comes when you think | |
# about which items torch needs to cache for the autograd, and which ones it | |
# can throw away). The numerical value of aux_loss as computed here will | |
# actually be larger than it should be, by limit * over_limit.sum(), but it | |
# has the same derivative as the real aux_loss which is penalty * (x.abs() - | |
# limit).relu(). | |
aux_loss = penalty * ((x_sign * over_limit).to(torch.int8) * x) | |
# note: we don't do sum() here on aux)_loss, but it's as if we had done | |
# sum() due to how with_loss() works. | |
x = with_loss(x, aux_loss) | |
# you must use x for something, or this will be ineffective. | |
return x | |
def _diag(x: Tensor): # like .diag(), but works for tensors with 3 dims. | |
if x.ndim == 2: | |
return x.diag() | |
else: | |
(batch, dim, dim) = x.shape | |
x = x.reshape(batch, dim * dim) | |
x = x[:, :: dim + 1] | |
assert x.shape == (batch, dim) | |
return x | |
def _whitening_metric(x: Tensor, num_groups: int): | |
""" | |
Computes the "whitening metric", a value which will be 1.0 if all the eigenvalues of | |
of the centered feature covariance are the same within each group's covariance matrix | |
and also between groups. | |
Args: | |
x: a Tensor of shape (*, num_channels) | |
num_groups: the number of groups of channels, a number >=1 that divides num_channels | |
Returns: | |
Returns a scalar Tensor that will be 1.0 if the data is "perfectly white" and | |
greater than 1.0 otherwise. | |
""" | |
assert x.dtype != torch.float16 | |
x = x.reshape(-1, x.shape[-1]) | |
(num_frames, num_channels) = x.shape | |
assert num_channels % num_groups == 0 | |
channels_per_group = num_channels // num_groups | |
x = x.reshape(num_frames, num_groups, channels_per_group).transpose(0, 1) | |
# x now has shape (num_groups, num_frames, channels_per_group) | |
# subtract the mean so we use the centered, not uncentered, covariance. | |
# My experience has been that when we "mess with the gradients" like this, | |
# it's better not do anything that tries to move the mean around, because | |
# that can easily cause instability. | |
x = x - x.mean(dim=1, keepdim=True) | |
# x_covar: (num_groups, channels_per_group, channels_per_group) | |
x_covar = torch.matmul(x.transpose(1, 2), x) | |
x_covar_mean_diag = _diag(x_covar).mean() | |
# the following expression is what we'd get if we took the matrix product | |
# of each covariance and measured the mean of its trace, i.e. | |
# the same as _diag(torch.matmul(x_covar, x_covar)).mean(). | |
x_covarsq_mean_diag = (x_covar ** 2).sum() / ( | |
num_groups * channels_per_group | |
) | |
# this metric will be >= 1.0; the larger it is, the less 'white' the data was. | |
metric = x_covarsq_mean_diag / (x_covar_mean_diag ** 2 + 1.0e-20) | |
return metric | |
class WhiteningPenaltyFunction(torch.autograd.Function): | |
def forward( | |
ctx, | |
x: Tensor, | |
num_groups: int, | |
whitening_limit: float, | |
grad_scale: float, | |
) -> Tensor: | |
ctx.save_for_backward(x) | |
ctx.num_groups = num_groups | |
ctx.whitening_limit = whitening_limit | |
ctx.grad_scale = grad_scale | |
return x | |
def backward(ctx, x_grad: Tensor): | |
(x_orig,) = ctx.saved_tensors | |
with torch.enable_grad(): | |
with torch.cuda.amp.autocast(enabled=False): | |
x_detached = x_orig.to(torch.float32).detach() | |
x_detached.requires_grad = True | |
metric = _whitening_metric(x_detached, ctx.num_groups) | |
if random.random() < 0.005 or __name__ == "__main__": | |
logging.info( | |
f"Whitening: num_groups={ctx.num_groups}, num_channels={x_orig.shape[-1]}, " | |
f"metric={metric.item():.2f} vs. limit={ctx.whitening_limit}" | |
) | |
(metric - ctx.whitening_limit).relu().backward() | |
penalty_grad = x_detached.grad | |
scale = ctx.grad_scale * ( | |
x_grad.to(torch.float32).norm() | |
/ (penalty_grad.norm() + 1.0e-20) | |
) | |
penalty_grad = penalty_grad * scale | |
return x_grad + penalty_grad.to(x_grad.dtype), None, None, None | |
class Whiten(nn.Module): | |
def __init__( | |
self, | |
num_groups: int, | |
whitening_limit: float, | |
prob: Union[float, Tuple[float, float]], | |
grad_scale: float, | |
): | |
""" | |
Args: | |
num_groups: the number of groups to divide the channel dim into before | |
whitening. We will attempt to make the feature covariance | |
within each group, after mean subtraction, as "white" as possible, | |
while having the same trace across all groups. | |
whitening_limit: a value greater than 1.0, that dictates how much | |
freedom we have to violate the constraints. 1.0 would mean perfectly | |
white, with exactly the same trace across groups; larger values | |
give more freedom. E.g. 2.0. | |
prob: the probability with which we apply the gradient modification | |
(also affects the grad scale). May be supplied as a float, | |
or as a pair (min_prob, max_prob) | |
grad_scale: determines the scale on the gradient term from this object, | |
relative to the rest of the gradient on the attention weights. | |
E.g. 0.02 (you may want to use smaller values than this if prob is large) | |
""" | |
super(Whiten, self).__init__() | |
assert num_groups >= 1 | |
assert whitening_limit >= 1 | |
assert grad_scale >= 0 | |
self.num_groups = num_groups | |
self.whitening_limit = whitening_limit | |
if isinstance(prob, float): | |
assert 0 < prob <= 1 | |
self.prob = prob | |
else: | |
(self.min_prob, self.max_prob) = prob | |
assert 0 < self.min_prob < self.max_prob <= 1 | |
self.prob = self.max_prob | |
self.grad_scale = grad_scale | |
def forward(self, x: Tensor) -> Tensor: | |
""" | |
In the forward pass, this function just returns the input unmodified. | |
In the backward pass, it will modify the gradients to ensure that the | |
distribution in each group has close to (lambda times I) as the covariance | |
after mean subtraction, with the same lambda across groups. | |
For whitening_limit > 1, there will be more freedom to violate this | |
constraint. | |
Args: | |
x: the input of shape (*, num_channels) | |
Returns: | |
x, unmodified. You should make sure | |
you use the returned value, or the graph will be freed | |
and nothing will happen in backprop. | |
""" | |
if ( | |
not x.requires_grad | |
or random.random() > self.prob | |
or self.grad_scale == 0 | |
): | |
return _no_op(x) | |
else: | |
if hasattr(self, "min_prob") and random.random() < 0.25: | |
# occasionally switch between min_prob and max_prob, based on whether | |
# we are above or below the threshold. | |
if ( | |
_whitening_metric(x.to(torch.float32), self.num_groups) | |
> self.whitening_limit | |
): | |
# there would be a change to the grad. | |
self.prob = self.max_prob | |
else: | |
self.prob = self.min_prob | |
return WhiteningPenaltyFunction.apply( | |
x, self.num_groups, self.whitening_limit, self.grad_scale | |
) | |
class WithLoss(torch.autograd.Function): | |
def forward(ctx, x: Tensor, y: Tensor): | |
ctx.y_shape = y.shape | |
return x | |
def backward(ctx, ans_grad: Tensor): | |
return ans_grad, torch.ones( | |
ctx.y_shape, dtype=ans_grad.dtype, device=ans_grad.device | |
) | |
def with_loss(x, y): | |
if torch.jit.is_scripting() or torch.jit.is_tracing(): | |
return x | |
# returns x but adds y.sum() to the loss function. | |
return WithLoss.apply(x, y) | |
def _no_op(x: Tensor) -> Tensor: | |
if torch.jit.is_scripting() or torch.jit.is_tracing(): | |
return x | |
else: | |
# a no-op function that will have a node in the autograd graph, | |
# to avoid certain bugs relating to backward hooks | |
return x.chunk(1, dim=-1)[0] | |
class Identity(torch.nn.Module): | |
def __init__(self): | |
super(Identity, self).__init__() | |
def forward(self, x): | |
return _no_op(x) | |
class MaxEig(torch.nn.Module): | |
""" | |
Modifies the backpropped derivatives of a function to try to discourage | |
that any given direction in activation space accounts for more than | |
a specified proportion of the covariance (e.g. 0.2). | |
Args: | |
num_channels: the number of channels | |
channel_dim: the dimension/axis corresponding to the channel, e.g. | |
-1, 0, 1, 2; will be interpreted as an offset from x.ndim if negative. | |
max_var_per_eig: the maximum proportion of the variance of the | |
features/channels, after mean subtraction, that can come from | |
any given eigenvalue. | |
min_prob: the minimum probability with which we apply this during any invocation | |
of forward(), assuming last time we applied the constraint it was | |
not active; supplied for speed. | |
scale: determines the scale with which we modify the gradients, relative | |
to the existing / unmodified gradients | |
""" | |
def __init__( | |
self, | |
num_channels: int, | |
channel_dim: int, | |
max_var_per_eig: float = 0.2, | |
min_prob: float = 0.01, | |
scale: float = 0.01, | |
): | |
super(MaxEig, self).__init__() | |
self.num_channels = num_channels | |
self.channel_dim = channel_dim | |
self.scale = scale | |
assert max_var_per_eig == 0.0 or max_var_per_eig > 1.0 / num_channels | |
self.max_var_per_eig = max_var_per_eig | |
# we figure out the dominant direction using the power method: starting with | |
# a random vector, keep multiplying by the covariance and renormalizing. | |
with torch.no_grad(): | |
# arbitrary.. would use randn() but want to leave the rest of the model's | |
# random parameters unchanged for comparison | |
direction = torch.arange(num_channels).to(torch.float) | |
direction = direction / direction.norm() | |
self.register_buffer("max_eig_direction", direction) | |
self.min_prob = min_prob | |
# cur_prob is the current probability we'll use to apply the ActivationBalancer. | |
# We'll regress this towards prob, each tiem we try to apply it and it is not | |
# active. | |
self.cur_prob = 1.0 | |
def forward(self, x: Tensor) -> Tensor: | |
if ( | |
torch.jit.is_scripting() | |
or self.max_var_per_eig <= 0 | |
or random.random() > self.cur_prob | |
or torch.jit.is_tracing() | |
): | |
return _no_op(x) | |
with torch.cuda.amp.autocast(enabled=False): | |
eps = 1.0e-20 | |
orig_x = x | |
x = x.to(torch.float32) | |
with torch.no_grad(): | |
x = x.transpose(self.channel_dim, -1).reshape( | |
-1, self.num_channels | |
) | |
x = x - x.mean(dim=0) | |
new_direction, coeffs = self._find_direction_coeffs( | |
x, self.max_eig_direction | |
) | |
x_var = (x ** 2).mean() | |
x_residual = x - coeffs * new_direction | |
x_residual_var = (x_residual ** 2).mean() | |
# `variance_proportion` is the proportion of the variance accounted for | |
# by the top eigen-direction. | |
variance_proportion = (x_var - x_residual_var) / ( | |
x_var + 1.0e-20 | |
) | |
# ensure new direction is nonzero even if x == 0, by including `direction`. | |
self._set_direction( | |
0.1 * self.max_eig_direction + new_direction | |
) | |
if random.random() < 0.01 or __name__ == "__main__": | |
logging.info( | |
f"variance_proportion = {variance_proportion.item()}, shape={tuple(orig_x.shape)}, cur_prob={self.cur_prob}" | |
) | |
if variance_proportion >= self.max_var_per_eig: | |
# The constraint is active. Note, we should quite rarely | |
# reach here, only near the beginning of training if we are | |
# starting to diverge, should this constraint be active. | |
cur_prob = self.cur_prob | |
self.cur_prob = ( | |
1.0 # next time, do the update with probability 1.0. | |
) | |
return MaxEigLimiterFunction.apply( | |
orig_x, coeffs, new_direction, self.channel_dim, self.scale | |
) | |
else: | |
# let self.cur_prob exponentially approach self.min_prob, as | |
# long as the constraint is inactive. | |
self.cur_prob = 0.75 * self.cur_prob + 0.25 * self.min_prob | |
return orig_x | |
def _set_direction(self, direction: Tensor): | |
""" | |
Sets self.max_eig_direction to a normalized version of `direction` | |
""" | |
direction = direction.detach() | |
direction = direction / direction.norm() | |
direction_sum = direction.sum().item() | |
if direction_sum - direction_sum == 0: # no inf/nan | |
self.max_eig_direction[:] = direction | |
else: | |
logging.info( | |
f"Warning: sum of direction in MaxEig is {direction_sum}, " | |
"num_channels={self.num_channels}, channel_dim={self.channel_dim}" | |
) | |
def _find_direction_coeffs( | |
self, x: Tensor, prev_direction: Tensor | |
) -> Tuple[Tensor, Tensor, Tensor]: | |
""" | |
Figure out (an approximation to) the proportion of the variance of a set of | |
feature vectors that can be attributed to the top eigen-direction. | |
Args: | |
x: a Tensor of shape (num_frames, num_channels), with num_frames > 1. | |
prev_direction: a Tensor of shape (num_channels,), that is our previous estimate | |
of the top eigen-direction, or a random direction if this is the first | |
iteration. Does not have to be normalized, but should be nonzero. | |
Returns: (cur_direction, coeffs), where: | |
cur_direction: a Tensor of shape (num_channels,) that is the current | |
estimate of the top eigen-direction. | |
coeffs: a Tensor of shape (num_frames, 1) that minimizes, or | |
approximately minimizes, (x - coeffs * cur_direction).norm() | |
""" | |
(num_frames, num_channels) = x.shape | |
assert num_channels > 1 and num_frames > 1 | |
assert prev_direction.shape == (num_channels,) | |
# `coeffs` are the coefficients of `prev_direction` in x. | |
# actually represent the coeffs up to a constant positive factor. | |
coeffs = (x * prev_direction).sum(dim=1, keepdim=True) + 1.0e-10 | |
cur_direction = (x * coeffs).sum(dim=0) / ( | |
(coeffs ** 2).sum() + 1.0e-20 | |
) | |
return cur_direction, coeffs | |
class DoubleSwishFunction(torch.autograd.Function): | |
""" | |
double_swish(x) = x * torch.sigmoid(x-1) | |
This is a definition, originally motivated by its close numerical | |
similarity to swish(swish(x)), where swish(x) = x * sigmoid(x). | |
Memory-efficient derivative computation: | |
double_swish(x) = x * s, where s(x) = torch.sigmoid(x-1) | |
double_swish'(x) = d/dx double_swish(x) = x * s'(x) + x' * s(x) = x * s'(x) + s(x). | |
Now, s'(x) = s(x) * (1-s(x)). | |
double_swish'(x) = x * s'(x) + s(x). | |
= x * s(x) * (1-s(x)) + s(x). | |
= double_swish(x) * (1-s(x)) + s(x) | |
... so we just need to remember s(x) but not x itself. | |
""" | |
def forward(ctx, x: Tensor) -> Tensor: | |
requires_grad = x.requires_grad | |
x_dtype = x.dtype | |
if x.dtype == torch.float16: | |
x = x.to(torch.float32) | |
s = torch.sigmoid(x - 1.0) | |
y = x * s | |
if requires_grad: | |
deriv = y * (1 - s) + s | |
# notes on derivative of x * sigmoid(x - 1): | |
# https://www.wolframalpha.com/input?i=d%2Fdx+%28x+*+sigmoid%28x-1%29%29 | |
# min \simeq -0.043638. Take floor as -0.043637 so it's a lower bund | |
# max \simeq 1.1990. Take ceil to be 1.2 so it's an upper bound. | |
# the combination of "+ torch.rand_like(deriv)" and casting to torch.uint8 (which | |
# floors), should be expectation-preserving. | |
floor = -0.043637 | |
ceil = 1.2 | |
d_scaled = (deriv - floor) * ( | |
255.0 / (ceil - floor) | |
) + torch.rand_like(deriv) | |
if __name__ == "__main__": | |
# for self-testing only. | |
assert d_scaled.min() >= 0.0 | |
assert d_scaled.max() < 256.0 | |
d_int = d_scaled.to(torch.uint8) | |
ctx.save_for_backward(d_int) | |
if x.dtype == torch.float16 or torch.is_autocast_enabled(): | |
y = y.to(torch.float16) | |
return y | |
def backward(ctx, y_grad: Tensor) -> Tensor: | |
(d,) = ctx.saved_tensors | |
# the same constants as used in forward pass. | |
floor = -0.043637 | |
ceil = 1.2 | |
d = d * ((ceil - floor) / 255.0) + floor | |
return y_grad * d | |
class DoubleSwish(torch.nn.Module): | |
def forward(self, x: Tensor) -> Tensor: | |
"""Return double-swish activation function which is an approximation to Swish(Swish(x)), | |
that we approximate closely with x * sigmoid(x-1). | |
""" | |
if torch.jit.is_scripting() or torch.jit.is_tracing(): | |
return x * torch.sigmoid(x - 1.0) | |
return DoubleSwishFunction.apply(x) | |
def BalancedDoubleSwish( | |
d_model, channel_dim=-1, max_abs=10.0, min_prob=0.25 | |
) -> nn.Sequential: | |
""" | |
ActivationBalancer -> DoubleSwish | |
""" | |
balancer = ActivationBalancer( | |
d_model, channel_dim=channel_dim, max_abs=max_abs, min_prob=min_prob | |
) | |
return nn.Sequential( | |
balancer, | |
DoubleSwish(), | |
) | |
def _test_max_eig(): | |
for proportion in [0.1, 0.5, 10.0]: | |
logging.info(f"proportion = {proportion}") | |
x = torch.randn(100, 128) | |
direction = torch.randn(128) | |
coeffs = torch.randn(100, 1) | |
x += proportion * direction * coeffs | |
x.requires_grad = True | |
num_channels = 128 | |
m = MaxEig( | |
num_channels, 1, 0.5, scale=0.1 # channel_dim # max_var_per_eig | |
) # grad_scale | |
for _ in range(4): | |
y = m(x) | |
y_grad = torch.randn_like(x) | |
y.backward(gradient=y_grad) | |
if proportion < 0.2: | |
assert torch.allclose(x.grad, y_grad, atol=1.0e-02) | |
elif proportion > 1.0: | |
assert not torch.allclose(x.grad, y_grad) | |
def _test_whiten(): | |
for proportion in [0.1, 0.5, 10.0]: | |
logging.info(f"_test_whiten(): proportion = {proportion}") | |
x = torch.randn(100, 128) | |
direction = torch.randn(128) | |
coeffs = torch.randn(100, 1) | |
x += proportion * direction * coeffs | |
x.requires_grad = True | |
num_channels = 128 | |
m = Whiten( | |
1, 5.0, prob=1.0, grad_scale=0.1 # num_groups # whitening_limit, | |
) # grad_scale | |
for _ in range(4): | |
y = m(x) | |
y_grad = torch.randn_like(x) | |
y.backward(gradient=y_grad) | |
if proportion < 0.2: | |
assert torch.allclose(x.grad, y_grad) | |
elif proportion > 1.0: | |
assert not torch.allclose(x.grad, y_grad) | |
def _test_activation_balancer_sign(): | |
probs = torch.arange(0, 1, 0.01) | |
N = 1000 | |
x = 1.0 * ( | |
(2.0 * (torch.rand(probs.numel(), N) < probs.unsqueeze(-1))) - 1.0 | |
) | |
x = x.detach() | |
x.requires_grad = True | |
m = ActivationBalancer( | |
probs.numel(), | |
channel_dim=0, | |
min_positive=0.05, | |
max_positive=0.95, | |
max_factor=0.2, | |
min_abs=0.0, | |
) | |
y_grad = torch.sign(torch.randn(probs.numel(), N)) | |
y = m(x) | |
y.backward(gradient=y_grad) | |
print("_test_activation_balancer_sign: x = ", x) | |
print("_test_activation_balancer_sign: y grad = ", y_grad) | |
print("_test_activation_balancer_sign: x grad = ", x.grad) | |
def _test_activation_balancer_magnitude(): | |
magnitudes = torch.arange(0, 1, 0.01) | |
N = 1000 | |
x = torch.sign(torch.randn(magnitudes.numel(), N)) * magnitudes.unsqueeze( | |
-1 | |
) | |
x = x.detach() | |
x.requires_grad = True | |
m = ActivationBalancer( | |
magnitudes.numel(), | |
channel_dim=0, | |
min_positive=0.0, | |
max_positive=1.0, | |
max_factor=0.2, | |
min_abs=0.2, | |
max_abs=0.8, | |
min_prob=1.0, | |
) | |
y_grad = torch.sign(torch.randn(magnitudes.numel(), N)) | |
y = m(x) | |
y.backward(gradient=y_grad) | |
print("_test_activation_balancer_magnitude: x = ", x) | |
print("_test_activation_balancer_magnitude: y grad = ", y_grad) | |
print("_test_activation_balancer_magnitude: x grad = ", x.grad) | |
def _test_basic_norm(): | |
num_channels = 128 | |
m = BasicNorm(num_channels=num_channels, channel_dim=1) | |
x = torch.randn(500, num_channels) | |
y = m(x) | |
assert y.shape == x.shape | |
x_rms = (x ** 2).mean().sqrt() | |
y_rms = (y ** 2).mean().sqrt() | |
print("x rms = ", x_rms) | |
print("y rms = ", y_rms) | |
assert y_rms < x_rms | |
assert y_rms > 0.5 * x_rms | |
def _test_double_swish_deriv(): | |
x = torch.randn(10, 12, dtype=torch.double) * 3.0 | |
x.requires_grad = True | |
m = DoubleSwish() | |
tol = (1.2 - (-0.043637)) / 255.0 | |
torch.autograd.gradcheck(m, x, atol=tol) | |
# for self-test. | |
x = torch.randn(1000, 1000, dtype=torch.double) * 3.0 | |
x.requires_grad = True | |
y = m(x) | |
def _test_softmax(): | |
a = torch.randn(2, 10, dtype=torch.float64) | |
b = a.clone() | |
a.requires_grad = True | |
b.requires_grad = True | |
a.softmax(dim=1)[:, 0].sum().backward() | |
print("a grad = ", a.grad) | |
softmax(b, dim=1)[:, 0].sum().backward() | |
print("b grad = ", b.grad) | |
assert torch.allclose(a.grad, b.grad) | |
if __name__ == "__main__": | |
logging.getLogger().setLevel(logging.INFO) | |
torch.set_num_threads(1) | |
torch.set_num_interop_threads(1) | |
_test_softmax() | |
_test_whiten() | |
_test_max_eig() | |
_test_activation_balancer_sign() | |
_test_activation_balancer_magnitude() | |
_test_basic_norm() | |
_test_double_swish_deriv() |