# 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 logging import random from typing import Optional, Tuple, Union import torch import torch.backends.cudnn.rnn as rnn import torch.nn as nn from torch import _VF, Tensor from icefall.utils import is_jit_tracing class ActivationBalancerFunction(torch.autograd.Function): @staticmethod 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 @staticmethod 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. """ @staticmethod 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 @staticmethod 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): @staticmethod 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 @staticmethod 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). """ @staticmethod def forward(ctx, x: Tensor, min_abs: float) -> Tensor: ctx.min_abs = min_abs return x @staticmethod 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. """ @staticmethod 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 @staticmethod 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): @staticmethod 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 @staticmethod 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 GradientFilterFunction(torch.autograd.Function): @staticmethod def forward( ctx, x: Tensor, batch_dim: int, # e.g., 1 threshold: float, # e.g., 10.0 *params: Tensor, # module parameters ) -> Tuple[Tensor, ...]: if x.requires_grad: if batch_dim < 0: batch_dim += x.ndim ctx.batch_dim = batch_dim ctx.threshold = threshold return (x,) + params @staticmethod def backward( ctx, x_grad: Tensor, *param_grads: Tensor, ) -> Tuple[Tensor, ...]: eps = 1.0e-20 dim = ctx.batch_dim norm_dims = [d for d in range(x_grad.ndim) if d != dim] norm_of_batch = (x_grad**2).mean(dim=norm_dims, keepdim=True).sqrt() median_norm = norm_of_batch.median() cutoff = median_norm * ctx.threshold inv_mask = (cutoff + norm_of_batch) / (cutoff + eps) mask = 1.0 / (inv_mask + eps) x_grad = x_grad * mask avg_mask = 1.0 / (inv_mask.mean() + eps) param_grads = [avg_mask * g for g in param_grads] return (x_grad, None, None) + tuple(param_grads) class GradientFilter(torch.nn.Module): """This is used to filter out elements that have extremely large gradients in batch and the module parameters with soft masks. Args: batch_dim (int): The batch dimension. threshold (float): For each element in batch, its gradient will be filtered out if the gradient norm is larger than `grad_norm_threshold * median`, where `median` is the median value of gradient norms of all elememts in batch. """ def __init__(self, batch_dim: int = 1, threshold: float = 10.0): super(GradientFilter, self).__init__() self.batch_dim = batch_dim self.threshold = threshold def forward(self, x: Tensor, *params: Tensor) -> Tuple[Tensor, ...]: if torch.jit.is_scripting() or is_jit_tracing(): return (x,) + params else: return GradientFilterFunction.apply( x, self.batch_dim, self.threshold, *params, ) 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 class ScaledEmbedding(nn.Module): r"""This is a modified version of nn.Embedding that introduces a learnable scale on the parameters. Note: due to how we initialize it, it's best used with schedulers like Noam that have a warmup period. It is a simple lookup table that stores embeddings of a fixed dictionary and size. This module is often used to store word embeddings and retrieve them using indices. The input to the module is a list of indices, and the output is the corresponding word embeddings. Args: num_embeddings (int): size of the dictionary of embeddings embedding_dim (int): the size of each embedding vector padding_idx (int, optional): If given, pads the output with the embedding vector at :attr:`padding_idx` (initialized to zeros) whenever it encounters the index. scale_grad_by_freq (boolean, optional): If given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default ``False``. sparse (bool, optional): If ``True``, gradient w.r.t. :attr:`weight` matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. initial_speed (float, optional): This affects how fast the parameter will learn near the start of training; you can set it to a value less than one if you suspect that a module is contributing to instability near the start of training. Note: regardless of the use of this option, it's best to use schedulers like Noam that have a warm-up period. Alternatively you can set it to more than 1 if you want it to initially train faster. Must be greater than 0. Attributes: weight (Tensor): the learnable weights of the module of shape (num_embeddings, embedding_dim) initialized from :math:`\mathcal{N}(0, 1)` Shape: - Input: :math:`(*)`, LongTensor of arbitrary shape containing the indices to extract - Output: :math:`(*, H)`, where `*` is the input shape and :math:`H=\text{embedding\_dim}` .. note:: Keep in mind that only a limited number of optimizers support sparse gradients: currently it's :class:`optim.SGD` (`CUDA` and `CPU`), :class:`optim.SparseAdam` (`CUDA` and `CPU`) and :class:`optim.Adagrad` (`CPU`) .. note:: With :attr:`padding_idx` set, the embedding vector at :attr:`padding_idx` is initialized to all zeros. However, note that this vector can be modified afterwards, e.g., using a customized initialization method, and thus changing the vector used to pad the output. The gradient for this vector from :class:`~torch.nn.Embedding` is always zero. Examples:: >>> # an Embedding module containing 10 tensors of size 3 >>> embedding = nn.Embedding(10, 3) >>> # a batch of 2 samples of 4 indices each >>> input = torch.LongTensor([[1,2,4,5],[4,3,2,9]]) >>> embedding(input) tensor([[[-0.0251, -1.6902, 0.7172], [-0.6431, 0.0748, 0.6969], [ 1.4970, 1.3448, -0.9685], [-0.3677, -2.7265, -0.1685]], [[ 1.4970, 1.3448, -0.9685], [ 0.4362, -0.4004, 0.9400], [-0.6431, 0.0748, 0.6969], [ 0.9124, -2.3616, 1.1151]]]) >>> # example with padding_idx >>> embedding = nn.Embedding(10, 3, padding_idx=0) >>> input = torch.LongTensor([[0,2,0,5]]) >>> embedding(input) tensor([[[ 0.0000, 0.0000, 0.0000], [ 0.1535, -2.0309, 0.9315], [ 0.0000, 0.0000, 0.0000], [-0.1655, 0.9897, 0.0635]]]) """ __constants__ = [ "num_embeddings", "embedding_dim", "padding_idx", "scale_grad_by_freq", "sparse", ] num_embeddings: int embedding_dim: int padding_idx: int scale_grad_by_freq: bool weight: Tensor sparse: bool def __init__( self, num_embeddings: int, embedding_dim: int, padding_idx: Optional[int] = None, scale_grad_by_freq: bool = False, sparse: bool = False, initial_speed: float = 1.0, ) -> None: super(ScaledEmbedding, self).__init__() self.num_embeddings = num_embeddings self.embedding_dim = embedding_dim if padding_idx is not None: if padding_idx > 0: assert ( padding_idx < self.num_embeddings ), "Padding_idx must be within num_embeddings" elif padding_idx < 0: assert ( padding_idx >= -self.num_embeddings ), "Padding_idx must be within num_embeddings" padding_idx = self.num_embeddings + padding_idx self.padding_idx = padding_idx self.scale_grad_by_freq = scale_grad_by_freq self.scale = nn.Parameter(torch.zeros(())) # see reset_parameters() self.sparse = sparse self.weight = nn.Parameter(torch.Tensor(num_embeddings, embedding_dim)) self.reset_parameters(initial_speed) def reset_parameters(self, initial_speed: float = 1.0) -> None: std = 0.1 / initial_speed nn.init.normal_(self.weight, std=std) nn.init.constant_(self.scale, torch.tensor(1.0 / std).log()) if self.padding_idx is not None: with torch.no_grad(): self.weight[self.padding_idx].fill_(0) def forward(self, input: Tensor) -> Tensor: F = torch.nn.functional scale = self.scale.exp() if input.numel() < self.num_embeddings: return ( F.embedding( input, self.weight, self.padding_idx, None, 2.0, # None, 2.0 relate to normalization self.scale_grad_by_freq, self.sparse, ) * scale ) else: return F.embedding( input, self.weight * scale, self.padding_idx, None, 2.0, # None, 2.0 relates to normalization self.scale_grad_by_freq, self.sparse, ) def extra_repr(self) -> str: # s = "{num_embeddings}, {embedding_dim}, scale={scale}" s = "{num_embeddings}, {embedding_dim}" if self.padding_idx is not None: s += ", padding_idx={padding_idx}" if self.scale_grad_by_freq is not False: s += ", scale_grad_by_freq={scale_grad_by_freq}" if self.sparse is not False: s += ", sparse=True" return s.format(**self.__dict__) 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.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, **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 ScaledLSTM(nn.LSTM): # See docs for ScaledLinear. # This class implements LSTM with scaling mechanism, using `torch._VF.lstm` # Please refer to https://github.com/pytorch/pytorch/blob/master/torch/nn/modules/rnn.py def __init__( self, *args, initial_scale: float = 1.0, initial_speed: float = 1.0, grad_norm_threshold: float = 10.0, **kwargs, ): super(ScaledLSTM, self).__init__(*args, **kwargs) initial_scale = torch.tensor(initial_scale).log() self._scales_names = [] self._scales = [] self.batch_dim = 0 if self.batch_first else 1 self.num_directions = 1 + int(self.bidirectional) for name in self._flat_weights_names: scale_name = name + "_scale" self._scales_names.append(scale_name) param = nn.Parameter(initial_scale.clone().detach()) setattr(self, scale_name, param) self._scales.append(param) self.grad_filter = GradientFilter( batch_dim=self.batch_dim, threshold=grad_norm_threshold ) self._reset_parameters( initial_speed ) # Overrides the reset_parameters in base class def _reset_parameters(self, initial_speed: float): std = 0.1 / initial_speed a = (3**0.5) * std scale = self.hidden_size**-0.5 v = scale / std for idx, name in enumerate(self._flat_weights_names): if "weight" in name: nn.init.uniform_(self._flat_weights[idx], -a, a) with torch.no_grad(): self._scales[idx] += torch.tensor(v).log() elif "bias" in name: nn.init.constant_(self._flat_weights[idx], 0.0) def _flatten_parameters(self, flat_weights) -> None: """Resets parameter data pointer so that they can use faster code paths. Right now, this works only if the module is on the GPU and cuDNN is enabled. Otherwise, it's a no-op. This function is modified from https://github.com/pytorch/pytorch/blob/master/torch/nn/modules/rnn.py # noqa """ # Short-circuits if _flat_weights is only partially instantiated if len(flat_weights) != len(self._flat_weights_names): return for w in flat_weights: if not isinstance(w, Tensor): return # Short-circuits if any tensor in flat_weights is not acceptable to cuDNN # or the tensors in flat_weights are of different dtypes first_fw = flat_weights[0] dtype = first_fw.dtype for fw in flat_weights: if ( not isinstance(fw.data, Tensor) or not (fw.data.dtype == dtype) or not fw.data.is_cuda or not torch.backends.cudnn.is_acceptable(fw.data) ): return # If any parameters alias, we fall back to the slower, copying code path. This is # a sufficient check, because overlapping parameter buffers that don't completely # alias would break the assumptions of the uniqueness check in # Module.named_parameters(). unique_data_ptrs = set(p.data_ptr() for p in flat_weights) if len(unique_data_ptrs) != len(flat_weights): return with torch.cuda.device_of(first_fw): # Note: no_grad() is necessary since _cudnn_rnn_flatten_weight is # an inplace operation on self._flat_weights with torch.no_grad(): if torch._use_cudnn_rnn_flatten_weight(): num_weights = 4 if self.bias else 2 if self.proj_size > 0: num_weights += 1 torch._cudnn_rnn_flatten_weight( flat_weights, num_weights, self.input_size, rnn.get_cudnn_mode(self.mode), self.hidden_size, self.proj_size, self.num_layers, self.batch_first, bool(self.bidirectional), ) def _get_flat_weights(self): """Get scaled weights, and resets their data pointer.""" flat_weights = [] for idx in range(len(self._flat_weights_names)): flat_weights.append(self._flat_weights[idx] * self._scales[idx].exp()) self._flatten_parameters(flat_weights) return flat_weights def forward(self, input: Tensor, hx: Optional[Tuple[Tensor, Tensor]] = None): # This function is modified from https://github.com/pytorch/pytorch/blob/master/torch/nn/modules/rnn.py # noqa # The change for calling `_VF.lstm()` is: # self._flat_weights -> self._get_flat_weights() if hx is None: h_zeros = torch.zeros( self.num_layers * self.num_directions, input.size(self.batch_dim), self.proj_size if self.proj_size > 0 else self.hidden_size, dtype=input.dtype, device=input.device, ) c_zeros = torch.zeros( self.num_layers * self.num_directions, input.size(self.batch_dim), self.hidden_size, dtype=input.dtype, device=input.device, ) hx = (h_zeros, c_zeros) self.check_forward_args(input, hx, None) flat_weights = self._get_flat_weights() input, *flat_weights = self.grad_filter(input, *flat_weights) result = _VF.lstm( input, hx, flat_weights, self.bias, self.num_layers, self.dropout, self.training, self.bidirectional, self.batch_first, ) output = result[0] hidden = result[1:] return output, hidden 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): @staticmethod 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 @staticmethod 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): @staticmethod def forward(ctx, x: Tensor, y: Tensor): ctx.y_shape = y.shape return x @staticmethod 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. """ @staticmethod 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 @staticmethod 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 _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()