# Copyright 2022-2025 Xiaomi Corp. (authors: Daniel Povey # Wei Kang) # # 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 math import random import sys from typing import Optional, Tuple, Union try: import k2 except Exception as e: logging.warning( f"Failed import k2 with error {e}. Swoosh functions will fallback to PyTorch" f" implementation, leading to slower speed and higher memory consumption." ) import torch import torch.nn as nn from torch import Tensor if torch.cuda.is_available(): DEVICE_TYPE = "cuda" elif torch.backends.mps.is_available(): DEVICE_TYPE = "mps" else: DEVICE_TYPE = "cpu" def get_memory_allocated(): if DEVICE_TYPE == "cuda": return torch.cuda.memory_allocated() elif DEVICE_TYPE == "mps": return torch.mps.current_allocated_memory() else: return 0 def custom_amp_decorator(dec, cuda_amp_deprecated): def decorator(func): return dec(func) if not cuda_amp_deprecated else dec(device_type=DEVICE_TYPE)(func) return decorator if hasattr(torch.amp, "custom_fwd"): deprecated = True from torch.amp import custom_bwd, custom_fwd else: deprecated = False from torch.cuda.amp import custom_bwd, custom_fwd custom_fwd = custom_amp_decorator(custom_fwd, deprecated) custom_bwd = custom_amp_decorator(custom_bwd, deprecated) def logaddexp_onnx(x: Tensor, y: Tensor) -> Tensor: max_value = torch.max(x, y) diff = torch.abs(x - y) return max_value + torch.log1p(torch.exp(-diff)) # RuntimeError: Exporting the operator logaddexp to ONNX opset version # 14 is not supported. Please feel free to request support or submit # a pull request on PyTorch GitHub. # # The following function is to solve the above error when exporting # models to ONNX via torch.jit.trace() def logaddexp(x: Tensor, y: Tensor) -> Tensor: # Caution(fangjun): Put torch.jit.is_scripting() before # torch.onnx.is_in_onnx_export(); # otherwise, it will cause errors for torch.jit.script(). # # torch.logaddexp() works for both torch.jit.script() and # torch.jit.trace() but it causes errors for ONNX export. # if torch.jit.is_scripting(): # Note: We cannot use torch.jit.is_tracing() here as it also # matches torch.onnx.export(). return torch.logaddexp(x, y) elif torch.onnx.is_in_onnx_export(): return logaddexp_onnx(x, y) else: # for torch.jit.trace() return torch.logaddexp(x, y) class PiecewiseLinear(object): """ Piecewise linear function, from float to float, specified as nonempty list of (x,y) pairs with the x values in order. x values <[initial x] or >[final x] are map to [initial y], [final y] respectively. """ def __init__(self, *args): assert len(args) >= 1, len(args) if len(args) == 1 and isinstance(args[0], PiecewiseLinear): self.pairs = list(args[0].pairs) else: self.pairs = [(float(x), float(y)) for x, y in args] for x, y in self.pairs: assert isinstance(x, (float, int)), type(x) assert isinstance(y, (float, int)), type(y) for i in range(len(self.pairs) - 1): assert self.pairs[i + 1][0] > self.pairs[i][0], ( i, self.pairs[i], self.pairs[i + 1], ) def __str__(self): # e.g. 'PiecewiseLinear((0., 10.), (100., 0.))' return f"PiecewiseLinear({str(self.pairs)[1:-1]})" def __call__(self, x): if x <= self.pairs[0][0]: return self.pairs[0][1] elif x >= self.pairs[-1][0]: return self.pairs[-1][1] else: cur_x, cur_y = self.pairs[0] for i in range(1, len(self.pairs)): next_x, next_y = self.pairs[i] if x >= cur_x and x <= next_x: return cur_y + (next_y - cur_y) * (x - cur_x) / (next_x - cur_x) cur_x, cur_y = next_x, next_y assert False def __mul__(self, alpha): return PiecewiseLinear(*[(x, y * alpha) for x, y in self.pairs]) def __add__(self, x): if isinstance(x, (float, int)): return PiecewiseLinear(*[(p[0], p[1] + x) for p in self.pairs]) s, x = self.get_common_basis(x) return PiecewiseLinear( *[(sp[0], sp[1] + xp[1]) for sp, xp in zip(s.pairs, x.pairs)] ) def max(self, x): if isinstance(x, (float, int)): x = PiecewiseLinear((0, x)) s, x = self.get_common_basis(x, include_crossings=True) return PiecewiseLinear( *[(sp[0], max(sp[1], xp[1])) for sp, xp in zip(s.pairs, x.pairs)] ) def min(self, x): if isinstance(x, float) or isinstance(x, int): x = PiecewiseLinear((0, x)) s, x = self.get_common_basis(x, include_crossings=True) return PiecewiseLinear( *[(sp[0], min(sp[1], xp[1])) for sp, xp in zip(s.pairs, x.pairs)] ) def __eq__(self, other): return self.pairs == other.pairs def get_common_basis(self, p: "PiecewiseLinear", include_crossings: bool = False): """ Returns (self_mod, p_mod) which are equivalent piecewise linear functions to self and p, but with the same x values. p: the other piecewise linear function include_crossings: if true, include in the x values positions where the functions indicate by this and p crosss. """ assert isinstance(p, PiecewiseLinear), type(p) # get sorted x-values without repetition. x_vals = sorted(set([x for x, _ in self.pairs] + [x for x, _ in p.pairs])) y_vals1 = [self(x) for x in x_vals] y_vals2 = [p(x) for x in x_vals] if include_crossings: extra_x_vals = [] for i in range(len(x_vals) - 1): if (y_vals1[i] > y_vals2[i]) != (y_vals1[i + 1] > y_vals2[i + 1]): # if the two lines in this subsegment potentially cross each other.. diff_cur = abs(y_vals1[i] - y_vals2[i]) diff_next = abs(y_vals1[i + 1] - y_vals2[i + 1]) # `pos`, between 0 and 1, gives the relative x position, # with 0 being x_vals[i] and 1 being x_vals[i+1]. pos = diff_cur / (diff_cur + diff_next) extra_x_val = x_vals[i] + pos * (x_vals[i + 1] - x_vals[i]) extra_x_vals.append(extra_x_val) if len(extra_x_vals) > 0: x_vals = sorted(set(x_vals + extra_x_vals)) y_vals1 = [self(x) for x in x_vals] y_vals2 = [p(x) for x in x_vals] return ( PiecewiseLinear(*zip(x_vals, y_vals1)), PiecewiseLinear(*zip(x_vals, y_vals2)), ) class ScheduledFloat(torch.nn.Module): """ This object is a torch.nn.Module only because we want it to show up in [top_level module].modules(); it does not have a working forward() function. You are supposed to cast it to float, as in, float(parent_module.whatever), and use it as something like a dropout prob. It is a floating point value whose value changes depending on the batch count of the training loop. It is a piecewise linear function where you specify the (x,y) pairs in sorted order on x; x corresponds to the batch index. For batch-index values before the first x or after the last x, we just use the first or last y value. Example: self.dropout = ScheduledFloat((0.0, 0.2), (4000.0, 0.0), default=0.0) `default` is used when self.batch_count is not set or not in training mode or in torch.jit scripting mode. """ def __init__(self, *args, default: float = 0.0): super().__init__() # self.batch_count and self.name will be written to in the training loop. self.batch_count = None self.name = None self.default = default self.schedule = PiecewiseLinear(*args) def extra_repr(self) -> str: return ( f"batch_count={self.batch_count}, schedule={str(self.schedule.pairs[1:-1])}" ) def __float__(self): batch_count = self.batch_count if ( batch_count is None or not self.training or torch.jit.is_scripting() or torch.jit.is_tracing() ): return float(self.default) else: ans = self.schedule(self.batch_count) if random.random() < 0.0002: logging.debug( f"ScheduledFloat: name={self.name}, " f"batch_count={self.batch_count}, ans={ans}" ) return ans def __add__(self, x): if isinstance(x, float) or isinstance(x, int): return ScheduledFloat(self.schedule + x, default=self.default) else: return ScheduledFloat( self.schedule + x.schedule, default=self.default + x.default ) def max(self, x): if isinstance(x, float) or isinstance(x, int): return ScheduledFloat(self.schedule.max(x), default=self.default) else: return ScheduledFloat( self.schedule.max(x.schedule), default=max(self.default, x.default), ) FloatLike = Union[float, ScheduledFloat] class CutoffEstimator: """ Estimates cutoffs of an arbitrary numerical quantity such that a specified proportion of items will be above the cutoff on average. p is the proportion of items that should be above the cutoff. """ def __init__(self, p: float): self.p = p # total count of items self.count = 0 # total count of items that were above the cutoff self.count_above = 0 # initial cutoff value self.cutoff = 0 def __call__(self, x: float) -> bool: """ Returns true if x is above the cutoff. """ ans = x > self.cutoff self.count += 1 if ans: self.count_above += 1 cur_p = self.count_above / self.count delta_p = cur_p - self.p if (delta_p > 0) == ans: q = abs(delta_p) self.cutoff = x * q + self.cutoff * (1 - q) return ans 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.amp.autocast(DEVICE_TYPE, 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 not x.requires_grad or torch.jit.is_scripting() or torch.jit.is_tracing(): return x.softmax(dim=dim) return SoftmaxFunction.apply(x, dim) class BiasNormFunction(torch.autograd.Function): # This computes: # scales = (torch.mean((x - bias) ** 2, keepdim=True)) ** -0.5 * log_scale.exp() # return x * scales # (after unsqueezing the bias), but it does it in a memory-efficient way so that # it can just store the returned value (chances are, this will also be needed for # some other reason, related to the next operation, so we can save memory). @staticmethod def forward( ctx, x: Tensor, bias: Tensor, log_scale: Tensor, channel_dim: int, store_output_for_backprop: bool, ) -> Tensor: assert bias.ndim == 1 if channel_dim < 0: channel_dim = channel_dim + x.ndim ctx.store_output_for_backprop = store_output_for_backprop ctx.channel_dim = channel_dim for _ in range(channel_dim + 1, x.ndim): bias = bias.unsqueeze(-1) scales = ( torch.mean((x - bias) ** 2, dim=channel_dim, keepdim=True) ** -0.5 ) * log_scale.exp() ans = x * scales ctx.save_for_backward( ans.detach() if store_output_for_backprop else x, scales.detach(), bias.detach(), log_scale.detach(), ) return ans @staticmethod def backward(ctx, ans_grad: Tensor) -> Tensor: ans_or_x, scales, bias, log_scale = ctx.saved_tensors if ctx.store_output_for_backprop: x = ans_or_x / scales else: x = ans_or_x x = x.detach() x.requires_grad = True bias.requires_grad = True log_scale.requires_grad = True with torch.enable_grad(): # recompute scales from x, bias and log_scale. scales = ( torch.mean((x - bias) ** 2, dim=ctx.channel_dim, keepdim=True) ** -0.5 ) * log_scale.exp() ans = x * scales ans.backward(gradient=ans_grad) return x.grad, bias.grad.flatten(), log_scale.grad, None, None class BiasNorm(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. Instead, we give the BiasNorm a trainable bias that it can use when computing the scale for normalization. We also give it a (scalar) trainable scale on the output. Args: num_channels: the number of channels, e.g. 512. channel_dim: the axis/dimension corresponding to the channel, interpreted as an offset from the input's ndim if negative. This is NOT the num_channels; it should typically be one of {-2, -1, 0, 1, 2, 3}. log_scale: the initial log-scale that we multiply the output by; this is learnable. log_scale_min: FloatLike, minimum allowed value of log_scale log_scale_max: FloatLike, maximum allowed value of log_scale store_output_for_backprop: only possibly affects memory use; recommend to set to True if you think the output of this module is more likely than the input of this module to be required to be stored for the backprop. """ def __init__( self, num_channels: int, channel_dim: int = -1, # CAUTION: see documentation. log_scale: float = 1.0, log_scale_min: float = -1.5, log_scale_max: float = 1.5, store_output_for_backprop: bool = False, ) -> None: super(BiasNorm, self).__init__() self.num_channels = num_channels self.channel_dim = channel_dim self.log_scale = nn.Parameter(torch.tensor(log_scale)) self.bias = nn.Parameter(torch.zeros(num_channels)) self.log_scale_min = log_scale_min self.log_scale_max = log_scale_max self.store_output_for_backprop = store_output_for_backprop def forward(self, x: Tensor) -> Tensor: assert x.shape[self.channel_dim] == self.num_channels if torch.jit.is_scripting() or torch.jit.is_tracing(): channel_dim = self.channel_dim if channel_dim < 0: channel_dim += x.ndim bias = self.bias for _ in range(channel_dim + 1, x.ndim): bias = bias.unsqueeze(-1) scales = ( torch.mean((x - bias) ** 2, dim=channel_dim, keepdim=True) ** -0.5 ) * self.log_scale.exp() return x * scales log_scale = limit_param_value( self.log_scale, min=float(self.log_scale_min), max=float(self.log_scale_max), training=self.training, ) return BiasNormFunction.apply( x, self.bias, log_scale, self.channel_dim, self.store_output_for_backprop, ) 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 class BalancerFunction(torch.autograd.Function): @staticmethod def forward( ctx, x: Tensor, min_mean: float, max_mean: float, min_rms: float, max_rms: float, grad_scale: float, channel_dim: int, ) -> Tensor: if channel_dim < 0: channel_dim += x.ndim ctx.channel_dim = channel_dim ctx.save_for_backward(x) ctx.config = ( min_mean, max_mean, min_rms, max_rms, grad_scale, channel_dim, ) return x @staticmethod def backward(ctx, x_grad: Tensor) -> Tuple[Tensor, None, None, None, None, None]: (x,) = ctx.saved_tensors ( min_mean, max_mean, min_rms, max_rms, grad_scale, channel_dim, ) = ctx.config try: with torch.enable_grad(): with torch.amp.autocast(DEVICE_TYPE, enabled=False): x = x.to(torch.float32) x = x.detach() x.requires_grad = True mean_dims = [i for i in range(x.ndim) if i != channel_dim] uncentered_var = (x**2).mean(dim=mean_dims, keepdim=True) mean = x.mean(dim=mean_dims, keepdim=True) stddev = (uncentered_var - (mean * mean)).clamp(min=1.0e-20).sqrt() rms = uncentered_var.clamp(min=1.0e-20).sqrt() m = mean / stddev # part of loss that relates to mean / stddev m_loss = (m - m.clamp(min=min_mean, max=max_mean)).abs() # put a much larger scale on the RMS-max-limit loss, so that if both # it and the m_loss are violated we fix the RMS loss first. rms_clamped = rms.clamp(min=min_rms, max=max_rms) r_loss = (rms_clamped / rms).log().abs() loss = m_loss + r_loss loss.backward(gradient=torch.ones_like(loss)) loss_grad = x.grad loss_grad_rms = ( (loss_grad**2) .mean(dim=mean_dims, keepdim=True) .sqrt() .clamp(min=1.0e-20) ) loss_grad = loss_grad * (grad_scale / loss_grad_rms) x_grad_float = x_grad.to(torch.float32) # scale each element of loss_grad by the absolute value of the # corresponding element of x_grad, which we view as a noisy estimate # of its magnitude for that (frame and dimension). later we can # consider factored versions. x_grad_mod = x_grad_float + (x_grad_float.abs() * loss_grad) x_grad = x_grad_mod.to(x_grad.dtype) except Exception as e: logging.info( f"Caught exception in Balancer backward: {e}, " f"size={list(x_grad.shape)}, will continue." ) return x_grad, None, None, None, None, None, None class Balancer(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. 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. 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. """ def __init__( self, num_channels: int, channel_dim: int, min_positive: FloatLike = 0.05, max_positive: FloatLike = 0.95, min_abs: FloatLike = 0.2, max_abs: FloatLike = 100.0, grad_scale: FloatLike = 0.04, prob: Optional[FloatLike] = None, ): super().__init__() if prob is None: prob = ScheduledFloat((0.0, 0.5), (8000.0, 0.125), default=0.4) self.prob = prob # 5% of the time we will return and do nothing because memory usage is # too high. self.mem_cutoff = CutoffEstimator(0.05) # actually self.num_channels is no longer needed except for an assertion. self.num_channels = num_channels self.channel_dim = channel_dim self.min_positive = min_positive self.max_positive = max_positive self.min_abs = min_abs self.max_abs = max_abs self.grad_scale = grad_scale def forward(self, x: Tensor) -> Tensor: if ( torch.jit.is_scripting() or not x.requires_grad or ((x.is_cuda or x.device.type == "mps") and self.mem_cutoff(get_memory_allocated())) ): return _no_op(x) prob = float(self.prob) if random.random() < prob: # The following inner-functions convert from the way we historically # specified these limitations, as limits on the absolute value and the # proportion of positive values, to limits on the RMS value and # the (mean / stddev). def _abs_to_rms(x): # for normally distributed data, if the expected absolute value is x, # the expected rms value will be sqrt(pi/2) * x. return 1.25331413732 * x def _proportion_positive_to_mean(x): def _atanh(x): eps = 1.0e-10 # eps is to prevent crashes if x is exactly 0 or 1. # we'll just end up returning a fairly large value. return (math.log(1 + x + eps) - math.log(1 - x + eps)) / 2.0 def _approx_inverse_erf(x): # 1 / (sqrt(pi) * ln(2)), # see https://math.stackexchange.com/questions/321569/ # approximating-the-error-function-erf-by-analytical-functions # this approximation is extremely crude and gets progressively worse # for x very close to -1 or +1, but we mostly care about the # "middle" region # e.g. _approx_inverse_erf(0.05) = 0.0407316414078772, # and math.erf(0.0407316414078772) = 0.045935330944660666, # which is pretty close to 0.05. return 0.8139535143 * _atanh(x) # first convert x from the range 0..1 to the range -1..1 which the error # function returns x = -1 + (2 * x) return _approx_inverse_erf(x) min_mean = _proportion_positive_to_mean(float(self.min_positive)) max_mean = _proportion_positive_to_mean(float(self.max_positive)) min_rms = _abs_to_rms(float(self.min_abs)) max_rms = _abs_to_rms(float(self.max_abs)) grad_scale = float(self.grad_scale) assert x.shape[self.channel_dim] == self.num_channels return BalancerFunction.apply( x, min_mean, max_mean, min_rms, max_rms, grad_scale, self.channel_dim, ) else: return _no_op(x) def penalize_abs_values_gt( x: Tensor, limit: float, penalty: float, name: str = None ) -> 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. The name is for randomly printed debug info. """ 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, name) # 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, module: nn.Module) -> Tensor: ctx.save_for_backward(x) ctx.module = module return x @staticmethod def backward(ctx, x_grad: Tensor): (x_orig,) = ctx.saved_tensors w = ctx.module try: with torch.enable_grad(): with torch.amp.autocast(DEVICE_TYPE, enabled=False): x_detached = x_orig.to(torch.float32).detach() x_detached.requires_grad = True metric = _whitening_metric(x_detached, w.num_groups) if random.random() < 0.005 or __name__ == "__main__": logging.debug( f"Whitening: name={w.name}, num_groups={w.num_groups}," f"num_channels={x_orig.shape[-1]}, " f"metric={metric.item():.2f}" f" vs. limit={float(w.whitening_limit)}" ) if metric < float(w.whitening_limit): w.prob = w.min_prob return x_grad, None else: w.prob = w.max_prob metric.backward() penalty_grad = x_detached.grad scale = w.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 except Exception as e: logging.info( f"Caught exception in Whiten backward: {e}, " f"size={list(x_grad.shape)}, will continue." ) return x_grad, None class Whiten(nn.Module): def __init__( self, num_groups: int, whitening_limit: FloatLike, prob: Union[float, Tuple[float, float]], grad_scale: FloatLike, ): """ 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 float(whitening_limit) >= 1 assert grad_scale >= 0 self.num_groups = num_groups self.whitening_limit = whitening_limit self.grad_scale = grad_scale if isinstance(prob, float): prob = (prob, prob) (self.min_prob, self.max_prob) = prob assert 0 < self.min_prob <= self.max_prob <= 1 self.prob = self.max_prob self.name = None # will be set in training loop 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. """ grad_scale = float(self.grad_scale) if not x.requires_grad or random.random() > self.prob or grad_scale == 0: return _no_op(x) else: return WhiteningPenaltyFunction.apply(x, self) class WithLoss(torch.autograd.Function): @staticmethod def forward(ctx, x: Tensor, y: Tensor, name: str): ctx.y_shape = y.shape if random.random() < 0.002 and name is not None: loss_sum = y.sum().item() logging.debug(f"WithLoss: name={name}, loss-sum={loss_sum:.3e}") 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), None, ) def with_loss(x, y, name): # returns x but adds y.sum() to the loss function. return WithLoss.apply(x, y, name) class LimitParamValue(torch.autograd.Function): @staticmethod def forward(ctx, x: Tensor, min: float, max: float): ctx.save_for_backward(x) assert max >= min ctx.min = min ctx.max = max return x @staticmethod def backward(ctx, x_grad: Tensor): (x,) = ctx.saved_tensors # where x < ctx.min, ensure all grads are negative (this will tend to make # x more positive). x_grad = x_grad * torch.where( torch.logical_and(x_grad > 0, x < ctx.min), -1.0, 1.0 ) # where x > ctx.max, ensure all grads are positive (this will tend to make # x more negative). x_grad *= torch.where(torch.logical_and(x_grad < 0, x > ctx.max), -1.0, 1.0) return x_grad, None, None def limit_param_value( x: Tensor, min: float, max: float, prob: float = 0.6, training: bool = True ): # You apply this to (typically) an nn.Parameter during training to ensure that its # (elements mostly) stays within a supplied range. This is done by modifying the # gradients in backprop. # It's not necessary to do this on every batch: do it only some of the time, # to save a little time. if training and random.random() < prob: return LimitParamValue.apply(x, min, max) else: return x 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] # Identity more friendly to backward hooks than nn.Identity(), for diagnostic reasons. class Identity(torch.nn.Module): def __init__(self): super(Identity, self).__init__() def forward(self, x): return _no_op(x) # Dropout2 is just like normal dropout, except it supports schedules # on the dropout rates. class Dropout2(nn.Module): def __init__(self, p: FloatLike): super().__init__() self.p = p def forward(self, x: Tensor) -> Tensor: return torch.nn.functional.dropout(x, p=float(self.p), training=self.training) class MulForDropout3(torch.autograd.Function): # returns (x * y * alpha) where alpha is a float and y doesn't require # grad and is zero-or-one. @staticmethod @custom_fwd def forward(ctx, x, y, alpha): assert not y.requires_grad ans = x * y * alpha ctx.save_for_backward(ans) ctx.alpha = alpha return ans @staticmethod @custom_bwd def backward(ctx, ans_grad): (ans,) = ctx.saved_tensors x_grad = ctx.alpha * ans_grad * (ans != 0) return x_grad, None, None # Dropout3 is just like normal dropout, except it supports schedules on the dropout # rates, and it lets you choose one dimension to share the dropout mask over class Dropout3(nn.Module): def __init__(self, p: FloatLike, shared_dim: int): super().__init__() self.p = p self.shared_dim = shared_dim def forward(self, x: Tensor) -> Tensor: p = float(self.p) if not self.training or p == 0: return _no_op(x) scale = 1.0 / (1 - p) rand_shape = list(x.shape) rand_shape[self.shared_dim] = 1 mask = torch.rand(*rand_shape, device=x.device) > p ans = MulForDropout3.apply(x, mask, scale) return ans class SwooshLFunction(torch.autograd.Function): """ swoosh_l(x) = log(1 + exp(x-4)) - 0.08*x - 0.035 """ @staticmethod def forward(ctx, x: Tensor) -> Tensor: requires_grad = x.requires_grad if x.dtype == torch.float16: x = x.to(torch.float32) zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) coeff = -0.08 with torch.amp.autocast(DEVICE_TYPE, enabled=False): with torch.enable_grad(): x = x.detach() x.requires_grad = True y = torch.logaddexp(zero, x - 4.0) + coeff * x - 0.035 if not requires_grad: return y y.backward(gradient=torch.ones_like(y)) grad = x.grad floor = coeff ceil = 1.0 + coeff + 0.005 d_scaled = (grad - floor) * (255.0 / (ceil - floor)) + torch.rand_like( grad ) 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. coeff = -0.08 floor = coeff ceil = 1.0 + coeff + 0.005 d = d * ((ceil - floor) / 255.0) + floor return y_grad * d class SwooshL(torch.nn.Module): def forward(self, x: Tensor) -> Tensor: """Return Swoosh-L activation.""" if torch.jit.is_scripting() or torch.jit.is_tracing(): zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) return logaddexp(zero, x - 4.0) - 0.08 * x - 0.035 elif "k2" not in sys.modules: return SwooshLFunction.apply(x) else: if not x.requires_grad: return k2.swoosh_l_forward(x) else: return k2.swoosh_l(x) class SwooshLOnnx(torch.nn.Module): def forward(self, x: Tensor) -> Tensor: """Return Swoosh-L activation.""" zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) return logaddexp_onnx(zero, x - 4.0) - 0.08 * x - 0.035 class SwooshRFunction(torch.autograd.Function): """ swoosh_r(x) = log(1 + exp(x-1)) - 0.08*x - 0.313261687 derivatives are between -0.08 and 0.92. """ @staticmethod def forward(ctx, x: Tensor) -> Tensor: requires_grad = x.requires_grad if x.dtype == torch.float16: x = x.to(torch.float32) zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) with torch.amp.autocast(DEVICE_TYPE, enabled=False): with torch.enable_grad(): x = x.detach() x.requires_grad = True y = torch.logaddexp(zero, x - 1.0) - 0.08 * x - 0.313261687 if not requires_grad: return y y.backward(gradient=torch.ones_like(y)) grad = x.grad floor = -0.08 ceil = 0.925 d_scaled = (grad - floor) * (255.0 / (ceil - floor)) + torch.rand_like( grad ) 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 = -0.08 ceil = 0.925 d = d * ((ceil - floor) / 255.0) + floor return y_grad * d class SwooshR(torch.nn.Module): def forward(self, x: Tensor) -> Tensor: """Return Swoosh-R activation.""" if torch.jit.is_scripting() or torch.jit.is_tracing(): zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) return logaddexp(zero, x - 1.0) - 0.08 * x - 0.313261687 elif "k2" not in sys.modules: return SwooshRFunction.apply(x) else: if not x.requires_grad: return k2.swoosh_r_forward(x) else: return k2.swoosh_r(x) class SwooshROnnx(torch.nn.Module): def forward(self, x: Tensor) -> Tensor: """Return Swoosh-R activation.""" zero = torch.tensor(0.0, dtype=x.dtype, device=x.device) return logaddexp_onnx(zero, x - 1.0) - 0.08 * x - 0.313261687 # simple version of SwooshL that does not redefine the backprop, used in # ActivationDropoutAndLinearFunction. def SwooshLForward(x: Tensor): with torch.amp.autocast(DEVICE_TYPE, enabled=False): x = x.to(torch.float32) x_offset = x - 4.0 log_sum = (1.0 + x_offset.exp()).log().to(x.dtype) log_sum = torch.where(log_sum == float("inf"), x_offset, log_sum) return log_sum - 0.08 * x - 0.035 # simple version of SwooshR that does not redefine the backprop, used in # ActivationDropoutAndLinearFunction. def SwooshRForward(x: Tensor): with torch.amp.autocast(DEVICE_TYPE, enabled=False): x = x.to(torch.float32) x_offset = x - 1.0 log_sum = (1.0 + x_offset.exp()).log().to(x.dtype) log_sum = torch.where(log_sum == float("inf"), x_offset, log_sum) return log_sum - 0.08 * x - 0.313261687 class ActivationDropoutAndLinearFunction(torch.autograd.Function): @staticmethod @custom_fwd def forward( ctx, x: Tensor, weight: Tensor, bias: Optional[Tensor], activation: str, dropout_p: float, dropout_shared_dim: Optional[int], ): if dropout_p != 0.0: dropout_shape = list(x.shape) if dropout_shared_dim is not None: dropout_shape[dropout_shared_dim] = 1 # else it won't be very memory efficient. dropout_mask = (1.0 / (1.0 - dropout_p)) * ( torch.rand(*dropout_shape, device=x.device, dtype=x.dtype) > dropout_p ) else: dropout_mask = None ctx.save_for_backward(x, weight, bias, dropout_mask) ctx.activation = activation forward_activation_dict = { "SwooshL": k2.swoosh_l_forward, "SwooshR": k2.swoosh_r_forward, } # it will raise a KeyError if this fails. This will be an error. We let it # propagate to the user. activation_func = forward_activation_dict[activation] x = activation_func(x) if dropout_mask is not None: x = x * dropout_mask x = torch.nn.functional.linear(x, weight, bias) return x @staticmethod @custom_bwd def backward(ctx, ans_grad: Tensor): saved = ctx.saved_tensors (x, weight, bias, dropout_mask) = saved forward_and_deriv_activation_dict = { "SwooshL": k2.swoosh_l_forward_and_deriv, "SwooshR": k2.swoosh_r_forward_and_deriv, } # the following lines a KeyError if the activation is unrecognized. # This will be an error. We let it propagate to the user. func = forward_and_deriv_activation_dict[ctx.activation] y, func_deriv = func(x) if dropout_mask is not None: y = y * dropout_mask # now compute derivative of y w.r.t. weight and bias.. # y: (..., in_channels), ans_grad: (..., out_channels), (out_channels, in_channels) = weight.shape in_channels = y.shape[-1] g = ans_grad.reshape(-1, out_channels) weight_deriv = torch.matmul(g.t(), y.reshape(-1, in_channels)) y_deriv = torch.matmul(ans_grad, weight) bias_deriv = None if bias is None else g.sum(dim=0) x_deriv = y_deriv * func_deriv if dropout_mask is not None: # order versus func_deriv does not matter x_deriv = x_deriv * dropout_mask return x_deriv, weight_deriv, bias_deriv, None, None, None class ActivationDropoutAndLinear(torch.nn.Module): """ This merges an activation function followed by dropout and then a nn.Linear module; it does so in a memory efficient way so that it only stores the input to the whole module. If activation == SwooshL and dropout_shared_dim != None, this will be equivalent to: nn.Sequential(SwooshL(), Dropout3(dropout_p, shared_dim=dropout_shared_dim), ScaledLinear(in_channels, out_channels, bias=bias, initial_scale=initial_scale)) If dropout_shared_dim is None, the dropout would be equivalent to Dropout2(dropout_p). Note: Dropout3 will be more memory efficient as the dropout mask is smaller. Args: in_channels: number of input channels, e.g. 256 out_channels: number of output channels, e.g. 256 bias: if true, have a bias activation: the activation function, for now just support SwooshL. dropout_p: the dropout probability or schedule (happens after nonlinearity). dropout_shared_dim: the dimension, if any, across which the dropout mask is shared (e.g. the time dimension). If None, this may be less memory efficient if there are modules before this one that cache the input for their backprop (e.g. Balancer or Whiten). """ def __init__( self, in_channels: int, out_channels: int, bias: bool = True, activation: str = "SwooshL", dropout_p: FloatLike = 0.0, dropout_shared_dim: Optional[int] = -1, initial_scale: float = 1.0, ): super().__init__() # create a temporary module of nn.Linear that we'll steal the # weights and bias from l = ScaledLinear( in_channels, out_channels, bias=bias, initial_scale=initial_scale ) self.weight = l.weight # register_parameter properly handles making it a parameter when l.bias # is None. I think there is some reason for doing it this way rather # than just setting it to None but I don't know what it is, maybe # something to do with exporting the module.. self.register_parameter("bias", l.bias) self.activation = activation self.dropout_p = dropout_p self.dropout_shared_dim = dropout_shared_dim def forward(self, x: Tensor): if ( torch.jit.is_scripting() or torch.jit.is_tracing() or "k2" not in sys.modules ): if self.activation == "SwooshL": x = SwooshLForward(x) elif self.activation == "SwooshR": x = SwooshRForward(x) else: assert False, self.activation return torch.nn.functional.linear(x, self.weight, self.bias) return ActivationDropoutAndLinearFunction.apply( x, self.weight, self.bias, self.activation, float(self.dropout_p), self.dropout_shared_dim, ) 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 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_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 = Balancer( probs.numel(), channel_dim=0, min_positive=0.05, max_positive=0.95, min_abs=0.0, prob=1.0, ) y_grad = torch.sign(torch.randn(probs.numel(), N)) y = m(x) y.backward(gradient=y_grad) print("_test_balancer_sign: x = ", x) print("_test_balancer_sign: y grad = ", y_grad) print("_test_balancer_sign: x grad = ", x.grad) def _test_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 = Balancer( magnitudes.numel(), channel_dim=0, min_positive=0.0, max_positive=1.0, min_abs=0.2, max_abs=0.7, prob=1.0, ) y_grad = torch.sign(torch.randn(magnitudes.numel(), N)) y = m(x) y.backward(gradient=y_grad) print("_test_balancer_magnitude: x = ", x) print("_test_balancer_magnitude: y grad = ", y_grad) print("_test_balancer_magnitude: x grad = ", x.grad) def _test_swooshl_deriv(): x = torch.randn(10, 12, dtype=torch.double) * 3.0 x.requires_grad = True m = SwooshL() tol = 1.0 / 255.0 torch.autograd.gradcheck(m, x, atol=tol, eps=0.01) # for self-test. x = torch.randn(1000, 1000, dtype=torch.double) * 3.0 x.requires_grad = True y = m(x) return y def _test_swooshr_deriv(): x = torch.randn(10, 12, dtype=torch.double) * 3.0 x.requires_grad = True m = SwooshR() tol = 1.0 / 255.0 torch.autograd.gradcheck(m, x, atol=tol, eps=0.01) # for self-test. x = torch.randn(1000, 1000, dtype=torch.double) * 3.0 x.requires_grad = True y = m(x) return y 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) def _test_piecewise_linear(): p = PiecewiseLinear((0, 10.0)) for x in [-100, 0, 100]: assert p(x) == 10.0 p = PiecewiseLinear((0, 10.0), (1, 0.0)) for x, y in [(-100, 10.0), (0, 10.0), (0.5, 5.0), (1, 0.0), (2, 0.0)]: print("x, y = ", x, y) assert p(x) == y, (x, p(x), y) q = PiecewiseLinear((0.5, 15.0), (0.6, 1.0)) x_vals = [-1.0, 0.0, 0.1, 0.2, 0.5, 0.6, 0.7, 0.9, 1.0, 2.0] pq = p.max(q) for x in x_vals: y1 = max(p(x), q(x)) y2 = pq(x) assert abs(y1 - y2) < 0.001 pq = p.min(q) for x in x_vals: y1 = min(p(x), q(x)) y2 = pq(x) assert abs(y1 - y2) < 0.001 pq = p + q for x in x_vals: y1 = p(x) + q(x) y2 = pq(x) assert abs(y1 - y2) < 0.001 def _test_activation_dropout_and_linear(): in_channels = 20 out_channels = 30 for bias in [True, False]: # actually we don't test for dropout_p != 0.0 because forward functions will # different answers. This is because we are using the k2 implementation of # swoosh_l an swoosh_r inside SwooshL() and SwooshR(), and they call randn() # internally, messing up the random state. for dropout_p in [0.0]: for activation in ["SwooshL", "SwooshR"]: m1 = nn.Sequential( SwooshL() if activation == "SwooshL" else SwooshR(), Dropout3(p=dropout_p, shared_dim=-1), ScaledLinear( in_channels, out_channels, bias=bias, initial_scale=0.5 ), ) m2 = ActivationDropoutAndLinear( in_channels, out_channels, bias=bias, initial_scale=0.5, activation=activation, dropout_p=dropout_p, ) with torch.no_grad(): m2.weight[:] = m1[2].weight if bias: m2.bias[:] = m1[2].bias # make sure forward gives same result. x1 = torch.randn(10, in_channels) x1.requires_grad = True # TEMP. assert torch.allclose( SwooshRFunction.apply(x1), SwooshRForward(x1), atol=1.0e-03 ) x2 = x1.clone().detach() x2.requires_grad = True seed = 10 torch.manual_seed(seed) y1 = m1(x1) y_grad = torch.randn_like(y1) y1.backward(gradient=y_grad) torch.manual_seed(seed) y2 = m2(x2) y2.backward(gradient=y_grad) print( f"bias = {bias}, dropout_p = {dropout_p}, activation = {activation}" ) print("y1 = ", y1) print("y2 = ", y2) assert torch.allclose(y1, y2, atol=0.02) assert torch.allclose(m1[2].weight.grad, m2.weight.grad, atol=1.0e-05) if bias: assert torch.allclose(m1[2].bias.grad, m2.bias.grad, atol=1.0e-05) print("x1.grad = ", x1.grad) print("x2.grad = ", x2.grad) def isclose(a, b): # return true if cosine similarity is > 0.9. return (a * b).sum() > 0.9 * ( (a**2).sum() * (b**2).sum() ).sqrt() # the SwooshL() implementation has a noisy gradient due to 1-byte # storage of it. assert isclose(x1.grad, x2.grad) if __name__ == "__main__": logging.getLogger().setLevel(logging.DEBUG) torch.set_num_threads(1) torch.set_num_interop_threads(1) _test_piecewise_linear() _test_softmax() _test_whiten() _test_balancer_sign() _test_balancer_magnitude() _test_swooshr_deriv() _test_swooshl_deriv() _test_activation_dropout_and_linear()