# 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 from itertools import repeat from typing import Optional, Tuple, Union from functools import reduce import logging import random import torch import torch.nn as nn import torch.nn.functional as F from torch import Tensor from torch.nn import Embedding as ScaledEmbedding def _ntuple(n): def parse(x): if isinstance(x, collections.Iterable): return x return tuple(repeat(x, n)) return parse _single = _ntuple(1) _pair = _ntuple(2) class ActivationBalancerFunction(torch.autograd.Function): @staticmethod def forward( ctx, x: Tensor, channel_dim: int, min_positive: float, # e.g. 0.05 max_positive: float, # e.g. 0.95 max_factor: float, # e.g. 0.01 min_abs: float, # e.g. 0.2 max_abs: float, # e.g. 100.0 ) -> Tensor: if x.requires_grad: if channel_dim < 0: channel_dim += x.ndim sum_dims = [d for d in range(x.ndim) if d != channel_dim] x_normalized = x - torch.mean(x, dim=sum_dims, keepdim=True) xgtmean = (x_normalized > 0) proportion_positive = torch.mean( (x > 0).to(x.dtype), dim=sum_dims, keepdim=True ) factor1 = ( (min_positive - proportion_positive).relu() * (max_factor / min_positive) if min_positive != 0.0 else 0.0 ) factor2 = ( (proportion_positive - max_positive).relu() * (max_factor / (max_positive - 1.0)) if max_positive != 1.0 else 0.0 ) # `factor` is a tensor of shape something like (1, 1, num_channels, # 1), containing elements between -1 and 1 that are zero if the # proportion of positive features is between min_positive and # max_positive, max_factor if proportion==0.0 (all features are negative), # and -max_factor if proportion==1.0 (all features are positive). It is # an amount per channel by which we'll modify the gradient; the sign # of modifying the gradient will depend on the sign of the gradient. factor = factor1 + factor2 if isinstance(factor, float): factor = torch.zeros_like(proportion_positive) mean_abs = torch.mean(x_normalized.abs(), dim=sum_dims, keepdim=True) below_threshold = mean_abs < min_abs above_threshold = mean_abs > max_abs ctx.save_for_backward( factor, xgtmean, below_threshold, above_threshold ) ctx.max_factor = max_factor ctx.sum_dims = sum_dims return x @staticmethod def backward( ctx, x_grad: Tensor ) -> Tuple[Tensor, None, None, None, None, None, None]: factor, xgtmean, below_threshold, above_threshold = ctx.saved_tensors dtype = x_grad.dtype scale_factor = ( (below_threshold.to(dtype) - above_threshold.to(dtype)) * (xgtmean.to(dtype) - 0.5) * (ctx.max_factor * 2.0) ) neg_delta_grad = x_grad.abs() * (factor + scale_factor) return x_grad - neg_delta_grad, None, None, None, None, None, None def find_direction_coeffs(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 MaxEigLimiterFunction(torch.autograd.Function): @staticmethod def forward( ctx, x: Tensor, direction: Tensor, channel_dim: int, prob: float, subtract_mean: bool, max_variance_proportion: float, grad_scale: float) -> Tuple[Tensor, Tensor]: if random.random() > prob: return x, direction eps = 1.0e-20 num_channels = x.shape[channel_dim] assert max_variance_proportion > 1.0 / num_channels orig_x = x x = x.transpose(channel_dim, -1).reshape(-1, num_channels) if subtract_mean: x = x - x.mean(dim=0) new_direction, coeffs = find_direction_coeffs(x, 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) ans_direction = direction + new_direction # ensure nonzero even if x == 0 ans_direction = ans_direction / ans_direction.norm() if random.random() < 0.0005: logging.info(f"variance_proportion = {variance_proportion.item()}, shape={tuple(x.shape)}") # Caution: this causes a CUDA sync, which is not ideal. if variance_proportion >= max_variance_proportion: ctx.channel_dim = channel_dim ctx.subtract_mean = subtract_mean ctx.grad_scale = grad_scale ctx.save_for_backward(orig_x.detach(), coeffs.detach(), new_direction.detach()) return orig_x, ans_direction @staticmethod def backward(ctx, x_grad, *args): # the *args is all the other derivs, which should be None or zero. if not hasattr(ctx, 'channel_dim'): # the top eig's proportion of the variance was below the threshold. return x_grad, None, None, None, None, None, None 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 if ctx.subtract_mean: 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, 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. """ def __init__( self, num_channels: int, channel_dim: int = -1, # CAUTION: see documentation. eps: float = 0.25, learn_eps: bool = True, ) -> 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()) def forward(self, x: Tensor) -> Tensor: assert x.shape[self.channel_dim] == self.num_channels scales = ( torch.mean(x ** 2, dim=self.channel_dim, keepdim=True) + self.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, **kwargs ) -> nn.Linear: """ 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, **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 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]. 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. max_var_per_eig: the maximum proportion of the variance of the features/channels, after mean subtraction, that can come from any given eigenvalue. """ def __init__( self, num_channels: int, channel_dim: int, min_positive: float = 0.05, max_positive: float = 0.95, max_factor: float = 0.01, min_abs: float = 0.2, max_abs: float = 100.0, max_var_per_eig: float = 0.0, ): 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 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 if max_var_per_eig > 0.0: 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) else: self.max_eig_direction = None def forward(self, x: Tensor) -> Tensor: if torch.jit.is_scripting(): return x if self.max_var_per_eig > 0: max_eig_prob = 0.25 with torch.cuda.amp.autocast(enabled=False): x, new_direction = MaxEigLimiterFunction.apply( x, self.max_eig_direction, self.channel_dim, max_eig_prob, True, # subtract_mean self.max_var_per_eig, self.max_factor / max_eig_prob, ) self.max_eig_direction[:] = new_direction.detach() return ActivationBalancerFunction.apply( x, self.channel_dim, self.min_positive, self.max_positive, self.max_factor, self.min_abs, self.max_abs, ) 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. """ @staticmethod def forward(ctx, x: Tensor) -> Tensor: x = x.detach() s = torch.sigmoid(x - 1.0) y = x * s ctx.save_for_backward(s, y) return y @staticmethod def backward(ctx, y_grad: Tensor) -> Tensor: s, y = ctx.saved_tensors return (y * (1 - s) + s) * y_grad 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(): return x * torch.sigmoid(x - 1.0) return DoubleSwishFunction.apply(x) def _test_max_eig_limiter(): 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 y, new_direction = MaxEigLimiterFunction.apply(x, direction, 1, # channel_dim 1.0, # prob True, # subtract_mean 0.5, # max_variance_proportion 0.1, # grad_scale ) cosine = (new_direction * direction).sum() / (new_direction.norm() * direction.norm()) logging.info(f"Direction cosine = {cosine}") 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 * (torch.rand(probs.numel(), N) < probs.unsqueeze(-1)) x = x.detach() x.requires_grad = True m = ActivationBalancer( probs.numel(), channel_dim=0, min_positive=0.05, max_positive=0.98, 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, ) 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) * 0.5 x.requires_grad = True m = DoubleSwish() torch.autograd.gradcheck(m, x) if __name__ == "__main__": logging.getLogger().setLevel(logging.INFO) torch.set_num_threads(1) torch.set_num_interop_threads(1) _test_max_eig_limiter() _test_activation_balancer_sign() _test_activation_balancer_magnitude() _test_basic_norm() _test_double_swish_deriv()