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658 lines
26 KiB
Python
658 lines
26 KiB
Python
# Copyright 2022 Xiaomi Corp. (authors: Daniel Povey)
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#
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# See ../LICENSE for clarification regarding multiple authors
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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from typing import List, Optional, Union, Tuple, List
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from lhotse.utils import fix_random_seed
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import torch
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from torch import Tensor
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from torch.optim import Optimizer
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class Cain(Optimizer):
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"""Implements Cain algorithm, which is a substantially modified form of the
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Adam optimizer.
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The modifications can be summarized as follows:
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(i) change Adam to what we called "Eve", which adds an extra configuration
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value, "target_rms" (default value: 0.1); and for non-scalar parameters,
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if their root-mean-square value exceeds "target_rms", we apply weight
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decay (aggressive enough weight decay that the rms stays at target_rms).
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This weight decay is applied in the same way as in AdamW, i.e. by
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parameter shrinkage rather than by modifying the gradients.
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(ii) By limiting the rms to 0.1, we reduce our modeling power; we restore
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it by replacing all weights and biases-- in fact, all model parameters--
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with expressions like
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weight * weight_scale.exp() or bias * bias_scale.exp().
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This has the benefit of making the learnable offsets and scales of
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BatchNorm/LayerNorm unnecessary.
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Below we describe the changes from Eve to Cain:
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(iii) We removed all the weight_scale and bias_scale parameters from
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the model and "moved them into the optimizer". Now we allow
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parameters to have any rms value (that's <= 10), but we:
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(a) make the update speed for a parameter proportional to
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its rms value.
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(b) Multiply the learning rate by 10 because we are getting rid of
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target_rms=0.1
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(c) simulate the effect of learning the weight_scale or bias_scale
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in log space using standard Adam, with a scale to prevent it
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from learning too fast. (see scale_exp_avg_sq in the
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code below).
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The original Adam algorithm was proposed in `Adam: A Method for Stochastic Optimization`_.
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The AdamW variant was proposed in `Decoupled Weight Decay Regularization`_.
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Eve is unpublished so far.
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Arguments:
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params (iterable): iterable of parameters to optimize or dicts defining
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parameter groups
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lr (float, optional): learning rate (default: 1e-3)
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betas (Tuple[float, float], optional): coefficients used for computing
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running averages of gradient and its square (default: (0.9, 0.999))
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eps (float, optional): term added to the denominator to improve
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numerical stability (default: 1e-8)
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scale_speed (float, optional): we multiply the learning rate by this value
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when learning (in log space) the scales of the parameter tensors
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rms_eps (float, optional): epsilon value such that when parameter
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rms value goes below this, we stop learning slower for that parameter,
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i.e. we treat the rms as if it were rms_eps. In practice, rms values
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will not go much below this.
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rms_max (float, optional): maximum root-mean-square value for
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non-scalar parameters, such that we don't let the parameter
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values exceed this; we'll shrink any parameter matrices that becomes
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larger than this.
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.. _Adam\: A Method for Stochastic Optimization:
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https://arxiv.org/abs/1412.6980
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.. _Decoupled Weight Decay Regularization:
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https://arxiv.org/abs/1711.05101
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.. _On the Convergence of Adam and Beyond:
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https://openreview.net/forum?id=ryQu7f-RZ
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"""
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def __init__(
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self,
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params,
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lr=1e-2,
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betas=(0.9, 0.98),
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eps=1e-8,
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scale_speed=0.05,
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rms_eps=1.0e-05,
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rms_max=10.0,
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):
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if not 0.0 <= lr:
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raise ValueError("Invalid learning rate: {}".format(lr))
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if not 0.0 <= eps:
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raise ValueError("Invalid epsilon value: {}".format(eps))
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if not 0.0 <= betas[0] < 1.0:
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raise ValueError(
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"Invalid beta parameter at index 0: {}".format(betas[0])
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)
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if not 0.0 <= betas[1] < 1.0:
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raise ValueError(
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"Invalid beta parameter at index 1: {}".format(betas[1])
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)
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if not 0 < scale_speed < 1.0:
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raise ValueError("Invalid scale_speed value: {}".format(scale_speed))
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if not 0.1 < rms_max <= 1000.0:
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raise ValueError("Invalid rms_max value: {}".format(rms_max))
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if not 0.0 < rms_eps < 0.1:
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raise ValueError("Invalid rms_eps value: {}".format(rms_eps))
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defaults = dict(
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lr=lr,
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betas=betas,
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eps=eps,
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scale_speed=0.05,
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rms_eps=rms_eps,
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rms_max=rms_max,
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)
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super(Cain, self).__init__(params, defaults)
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def __setstate__(self, state):
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super(Cain, self).__setstate__(state)
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@torch.no_grad()
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def step(self, closure=None):
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"""Performs a single optimization step.
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Arguments:
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closure (callable, optional): A closure that reevaluates the model
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and returns the loss.
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"""
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loss = None
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if closure is not None:
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with torch.enable_grad():
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loss = closure()
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for group in self.param_groups:
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beta1, beta2 = group["betas"]
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lr = group["lr"]
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scale_speed = group["scale_speed"]
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rms_eps = group["rms_eps"]
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eps = group["eps"]
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rms_max = group["rms_max"]
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for p in group["params"]:
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if p.grad is None:
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continue
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# Perform optimization step
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grad = p.grad
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if grad.is_sparse:
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raise RuntimeError(
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"AdamW does not support sparse gradients"
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)
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state = self.state[p]
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# State initialization
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if len(state) == 0:
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state["step"] = 0
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# Exponential moving average of gradient values
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state["delta"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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# Exponential moving average of squared gradient values
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state["exp_avg_sq"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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if p.numel() > 1:
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# we keep track of the RMS value of the parameters to
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# help set the learning rate... this emulates Eve.
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state["param_rms"] = (p**2).mean().sqrt()
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# we learn the scale on the parameters in a way
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# that also emulates Eve.
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state["scale_exp_avg_sq"] = torch.zeros((), device=p.device,
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dtype=p.dtype)
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delta, exp_avg_sq = state["delta"], state["exp_avg_sq"]
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step = state["step"]
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delta.mul_(beta1)
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if p.numel() > 1:
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if step % 10 == 0:
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state["param_rms"].fill_((p**2).mean().sqrt())
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if True:
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# This block learns the scale on the parameters.
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# scale_deriv is the derivative w.r.t. a log-space scale
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# on the parameters, i.e. if we imagine: p =
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# underlying_param * scale.exp(), scale_deriv is the
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# derivative w.r.t. scale (it does not matter
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# what value `scale` currently has).
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scale_deriv = (p * grad).sum()
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scale_exp_avg_sq = state["scale_exp_avg_sq"]
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scale_exp_avg_sq.mul_(beta2).addcmul_(scale_deriv, scale_deriv,
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value=1 - beta2)
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# should actually be step + 1, so on 1st minibatch we are not learning
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# anything here. May fix this at some point.
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scale_bias_correction2 = 1 - beta2 ** (step + 1)
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scale_denom = (scale_exp_avg_sq.sqrt()).add_(eps)
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scale_alpha = -lr * (scale_bias_correction2 ** 0.5) * scale_speed * (1-beta1)
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# scale_delta is going to be the change in log-scale (before momentum), i.e. if
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# p = underlying_param * scale.exp(),
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# delta is the change in `scale`.
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scale_delta = scale_alpha * (scale_deriv / scale_denom)
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# the following is equivalent to:
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# if torch.all(state["param_rms"] > rms_max):
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# delta = -1.0e-03
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# which means: if the parameter root-mean-square value goes above the
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# specified limit, start to decay the parameters (and ignore the computed
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# delta).
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scale_delta = torch.where(state["param_rms"] > rms_max,
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torch.tensor(-1.0e-03 * (1-beta1),
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device=scale_delta.device,
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dtype=scale_delta.dtype),
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scale_delta)
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delta.add_(p, alpha=scale_delta)
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# Decay the second moment running average coefficient
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exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
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bias_correction2 = 1 - beta2 ** step
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grad_rms = (exp_avg_sq.sqrt()).add_(eps)
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this_delta = grad / grad_rms
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this_lr = state["param_rms"].clamp(min=rms_eps) * lr * bias_correction2
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alpha = -(1-beta1) * this_lr
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# below, will do: delta.add_(this_delta, alpha=alpha)
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else:
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# p.numel() == 1
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# Decay the second moment running average coefficient
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exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
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bias_correction2 = 1 - beta2 ** step
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denom = (exp_avg_sq.sqrt()).add_(eps)
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this_delta = grad / denom
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alpha = -lr*(1-beta1)*(bias_correction2 ** 0.5)
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delta.add_(this_delta, alpha=alpha)
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p.add_(delta)
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state["step"] += 1
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return loss
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class LRScheduler(object):
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"""
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Base-class for learning rate schedulers where the learning-rate depends on both the
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batch and the epoch.
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"""
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def __init__(self, optimizer: Optimizer, verbose: bool = False):
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# Attach optimizer
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if not isinstance(optimizer, Optimizer):
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raise TypeError(
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"{} is not an Optimizer".format(type(optimizer).__name__)
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)
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self.optimizer = optimizer
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self.verbose = verbose
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for group in optimizer.param_groups:
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group.setdefault("initial_lr", group["lr"])
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self.base_lrs = [
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group["initial_lr"] for group in optimizer.param_groups
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]
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self.epoch = 0
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self.batch = 0
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def state_dict(self):
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"""Returns the state of the scheduler as a :class:`dict`.
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It contains an entry for every variable in self.__dict__ which
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is not the optimizer.
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"""
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return {
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"base_lrs": self.base_lrs,
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"epoch": self.epoch,
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"batch": self.batch,
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}
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def load_state_dict(self, state_dict):
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"""Loads the schedulers state.
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Args:
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state_dict (dict): scheduler state. Should be an object returned
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from a call to :meth:`state_dict`.
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"""
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self.__dict__.update(state_dict)
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def get_last_lr(self) -> List[float]:
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"""Return last computed learning rate by current scheduler. Will be a list of float."""
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return self._last_lr
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def get_lr(self):
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# Compute list of learning rates from self.epoch and self.batch and
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# self.base_lrs; this must be overloaded by the user.
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# e.g. return [some_formula(self.batch, self.epoch, base_lr) for base_lr in self.base_lrs ]
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raise NotImplementedError
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def step_batch(self, batch: Optional[int] = None) -> None:
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# Step the batch index, or just set it. If `batch` is specified, it
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# must be the batch index from the start of training, i.e. summed over
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# all epochs.
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# You can call this in any order; if you don't provide 'batch', it should
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# of course be called once per batch.
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if batch is not None:
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self.batch = batch
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else:
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self.batch = self.batch + 1
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self._set_lrs()
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def step_epoch(self, epoch: Optional[int] = None):
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# Step the epoch index, or just set it. If you provide the 'epoch' arg,
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# you should call this at the start of the epoch; if you don't provide the 'epoch'
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# arg, you should call it at the end of the epoch.
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if epoch is not None:
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self.epoch = epoch
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else:
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self.epoch = self.epoch + 1
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self._set_lrs()
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def _set_lrs(self):
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values = self.get_lr()
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assert len(values) == len(self.optimizer.param_groups)
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for i, data in enumerate(zip(self.optimizer.param_groups, values)):
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param_group, lr = data
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param_group["lr"] = lr
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self.print_lr(self.verbose, i, lr)
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self._last_lr = [group["lr"] for group in self.optimizer.param_groups]
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def print_lr(self, is_verbose, group, lr):
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"""Display the current learning rate."""
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if is_verbose:
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print(
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f"Epoch={self.epoch}, batch={self.batch}: adjusting learning rate"
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f" of group {group} to {lr:.4e}."
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)
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class Eve(Optimizer):
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"""
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Implements Eve algorithm. This is a modified version of AdamW with a special
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way of setting the weight-decay / shrinkage-factor, which is designed to make the
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rms of the parameters approach a particular target_rms (default: 0.1). This is
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for use with networks with 'scaled' versions of modules (see scaling.py), which
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will be close to invariant to the absolute scale on the parameter matrix.
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The original Adam algorithm was proposed in `Adam: A Method for Stochastic Optimization`_.
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The AdamW variant was proposed in `Decoupled Weight Decay Regularization`_.
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Eve is unpublished so far.
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Arguments:
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params (iterable): iterable of parameters to optimize or dicts defining
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parameter groups
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lr (float, optional): learning rate (default: 1e-3)
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betas (Tuple[float, float], optional): coefficients used for computing
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running averages of gradient and its square (default: (0.9, 0.999))
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eps (float, optional): term added to the denominator to improve
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numerical stability (default: 1e-8)
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weight_decay (float, optional): weight decay coefficient (default: 3e-4;
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this value means that the weight would decay significantly after
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about 3k minibatches. Is not multiplied by learning rate, but
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is conditional on RMS-value of parameter being > target_rms.
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target_rms (float, optional): target root-mean-square value of
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parameters, if they fall below this we will stop applying weight decay.
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.. _Adam\: A Method for Stochastic Optimization:
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https://arxiv.org/abs/1412.6980
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.. _Decoupled Weight Decay Regularization:
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https://arxiv.org/abs/1711.05101
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.. _On the Convergence of Adam and Beyond:
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https://openreview.net/forum?id=ryQu7f-RZ
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"""
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def __init__(
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self,
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params,
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lr=1e-3,
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betas=(0.9, 0.98),
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eps=1e-8,
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weight_decay=1e-3,
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target_rms=0.1,
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):
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if not 0.0 <= lr:
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raise ValueError("Invalid learning rate: {}".format(lr))
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if not 0.0 <= eps:
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raise ValueError("Invalid epsilon value: {}".format(eps))
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if not 0.0 <= betas[0] < 1.0:
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raise ValueError(
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"Invalid beta parameter at index 0: {}".format(betas[0])
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)
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if not 0.0 <= betas[1] < 1.0:
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raise ValueError(
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"Invalid beta parameter at index 1: {}".format(betas[1])
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)
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if not 0 <= weight_decay <= 0.1:
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raise ValueError(
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"Invalid weight_decay value: {}".format(weight_decay)
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)
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if not 0 < target_rms <= 10.0:
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raise ValueError("Invalid target_rms value: {}".format(target_rms))
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defaults = dict(
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lr=lr,
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betas=betas,
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eps=eps,
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weight_decay=weight_decay,
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target_rms=target_rms,
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)
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super(Eve, self).__init__(params, defaults)
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def __setstate__(self, state):
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super(Eve, self).__setstate__(state)
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@torch.no_grad()
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def step(self, closure=None):
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"""Performs a single optimization step.
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Arguments:
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closure (callable, optional): A closure that reevaluates the model
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and returns the loss.
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"""
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loss = None
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if closure is not None:
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with torch.enable_grad():
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loss = closure()
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for group in self.param_groups:
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for p in group["params"]:
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if p.grad is None:
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continue
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# Perform optimization step
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grad = p.grad
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if grad.is_sparse:
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raise RuntimeError(
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"AdamW does not support sparse gradients"
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)
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state = self.state[p]
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# State initialization
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if len(state) == 0:
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state["step"] = 0
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# Exponential moving average of gradient values
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state["exp_avg"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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# Exponential moving average of squared gradient values
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state["exp_avg_sq"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
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beta1, beta2 = group["betas"]
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state["step"] += 1
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bias_correction1 = 1 - beta1 ** state["step"]
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bias_correction2 = 1 - beta2 ** state["step"]
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# Decay the first and second moment running average coefficient
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exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
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exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
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denom = (exp_avg_sq.sqrt() * (bias_correction2 ** -0.5)).add_(
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group["eps"]
|
|
)
|
|
|
|
step_size = group["lr"] / bias_correction1
|
|
target_rms = group["target_rms"]
|
|
weight_decay = group["weight_decay"]
|
|
|
|
if p.numel() > 1:
|
|
# avoid applying this weight-decay on "scaling factors"
|
|
# (which are scalar).
|
|
is_above_target_rms = p.norm() > (
|
|
target_rms * (p.numel() ** 0.5)
|
|
)
|
|
p.mul_(1 - (weight_decay * is_above_target_rms))
|
|
|
|
p.addcdiv_(exp_avg, denom, value=-step_size)
|
|
|
|
return loss
|
|
|
|
|
|
class Eden(LRScheduler):
|
|
"""
|
|
Eden scheduler.
|
|
lr = initial_lr * (((batch**2 + lr_batches**2) / lr_batches**2) ** -0.25 *
|
|
(((epoch**2 + lr_epochs**2) / lr_epochs**2) ** -0.25))
|
|
|
|
E.g. suggest initial-lr = 0.003 (passed to optimizer).
|
|
|
|
Args:
|
|
optimizer: the optimizer to change the learning rates on
|
|
lr_batches: the number of batches after which we start significantly
|
|
decreasing the learning rate, suggest 5000.
|
|
lr_epochs: the number of epochs after which we start significantly
|
|
decreasing the learning rate, suggest 6 if you plan to do e.g.
|
|
20 to 40 epochs, but may need smaller number if dataset is huge
|
|
and you will do few epochs.
|
|
"""
|
|
|
|
def __init__(
|
|
self,
|
|
optimizer: Optimizer,
|
|
lr_batches: Union[int, float],
|
|
lr_epochs: Union[int, float],
|
|
verbose: bool = False,
|
|
):
|
|
super(Eden, self).__init__(optimizer, verbose)
|
|
self.lr_batches = lr_batches
|
|
self.lr_epochs = lr_epochs
|
|
|
|
def get_lr(self):
|
|
factor = (
|
|
(self.batch ** 2 + self.lr_batches ** 2) / self.lr_batches ** 2
|
|
) ** -0.25 * (
|
|
((self.epoch ** 2 + self.lr_epochs ** 2) / self.lr_epochs ** 2)
|
|
** -0.25
|
|
)
|
|
return [x * factor for x in self.base_lrs]
|
|
|
|
|
|
def _test_eden():
|
|
m = torch.nn.Linear(100, 100)
|
|
optim = Cain(m.parameters(), lr=0.003)
|
|
|
|
scheduler = Eden(optim, lr_batches=30, lr_epochs=2, verbose=True)
|
|
|
|
for epoch in range(10):
|
|
scheduler.step_epoch(epoch) # sets epoch to `epoch`
|
|
|
|
for step in range(20):
|
|
x = torch.randn(200, 100).detach()
|
|
x.requires_grad = True
|
|
y = m(x)
|
|
dy = torch.randn(200, 100).detach()
|
|
f = (y * dy).sum()
|
|
f.backward()
|
|
|
|
optim.step()
|
|
scheduler.step_batch()
|
|
optim.zero_grad()
|
|
|
|
print("last lr = ", scheduler.get_last_lr())
|
|
print("state dict = ", scheduler.state_dict())
|
|
|
|
|
|
def _test_eve_cain():
|
|
import timeit
|
|
from scaling import ScaledLinear
|
|
E = 100
|
|
B = 4
|
|
T = 2
|
|
print("in test_eve_cain")
|
|
device = torch.device('cuda')
|
|
dtype = torch.float32
|
|
|
|
# these input_magnitudes and output_magnitudes are to test that
|
|
# Abel is working as we expect and is able to adjust scales of
|
|
# different dims differently.
|
|
input_magnitudes = (1.0 * torch.randn(E, dtype=dtype, device=device)).exp()
|
|
output_magnitudes = (1.0 * torch.randn(E, dtype=dtype, device=device)).exp()
|
|
|
|
for iter in [1,0]:
|
|
fix_random_seed(42)
|
|
Linear = torch.nn.Linear if iter == 0 else ScaledLinear
|
|
m = torch.nn.Sequential(Linear(E, 200),
|
|
torch.nn.ReLU(),
|
|
Linear(200, E)).to(device)
|
|
|
|
train_pairs = [ (100.0 * torch.randn(B, T, E, device=device, dtype=dtype) * input_magnitudes,
|
|
torch.randn(B, T, E, device=device, dtype=dtype) * output_magnitudes) for _ in range(20) ]
|
|
|
|
if iter == 0: optim = Eve(m.parameters(), lr=0.003)
|
|
elif iter == 1: optim = Cain(m.parameters(), lr=0.03)
|
|
scheduler = Eden(optim, lr_batches=200, lr_epochs=10, verbose=False)
|
|
|
|
start = timeit.default_timer()
|
|
for epoch in range(150):
|
|
scheduler.step_epoch()
|
|
for n, (x,y) in enumerate(train_pairs):
|
|
y_out = m(x)
|
|
loss = ((y_out - y)**2).mean() * 100.0
|
|
if n == 0 and epoch % 10 == 0:
|
|
norm1 = '%.2e' % (m[0].weight**2).mean().sqrt().item()
|
|
norm1b = '%.2e' % (m[0].bias**2).mean().sqrt().item()
|
|
norm2 = '%.2e' % (m[2].weight**2).mean().sqrt().item()
|
|
norm2b = '%.2e' % (m[2].bias**2).mean().sqrt().item()
|
|
#scale1 = '%.2e' % (m[0].weight_scale.exp().item())
|
|
#scale1b = '%.2e' % (m[0].bias_scale.exp().item())
|
|
#scale2 = '%.2e' % (m[2].weight_scale.exp().item())
|
|
#scale2b = '%.2e' % (m[2].bias_scale.exp().item())
|
|
print(f"Iter {iter}, epoch {epoch}, batch {n}, loss {loss.item()}, norms={norm1,norm1b,norm2,norm2b}") # scales={scale1,scale1b,scale2,scale2b}
|
|
loss.log().backward()
|
|
optim.step()
|
|
optim.zero_grad()
|
|
scheduler.step_batch()
|
|
|
|
stop = timeit.default_timer()
|
|
print(f"Iter={iter}, Time taken: {stop - start}")
|
|
|
|
print("last lr = ", scheduler.get_last_lr())
|
|
#print("state dict = ", scheduler.state_dict())
|
|
#print("optim state_dict = ", optim.state_dict())
|
|
print("input_magnitudes = ", input_magnitudes)
|
|
print("output_magnitudes = ", output_magnitudes)
|
|
|
|
def stddev(x):
|
|
return ((x-x.mean())**2).mean().sqrt()
|
|
print("Un-normalized input col magnitudes log-stddev: ", stddev((m[0].weight**2).sum(dim=0).sqrt().log()))
|
|
print("Normalized input col magnitudes log-stddev: ", stddev(((m[0].weight**2).sum(dim=0).sqrt() * input_magnitudes).log()))
|
|
|
|
print("Un-normalized 0-output row magnitudes log-stddev: ", stddev((m[0].weight**2).sum(dim=1).sqrt().log()))
|
|
print("Un-normalized 2-input col magnitudes log-stddev: ", stddev((m[2].weight**2).sum(dim=0).sqrt().log()))
|
|
print("Un-normalized 2-output row magnitudes log-stddev: ", stddev((m[2].weight**2).sum(dim=1).sqrt().log()))
|
|
|
|
print("Normalized output row magnitudes log-stddev: ", stddev(((m[2].weight**2).sum(dim=1).sqrt() / output_magnitudes).log()))
|
|
|
|
|
|
|
|
if __name__ == "__main__":
|
|
torch.set_num_threads(1)
|
|
torch.set_num_interop_threads(1)
|
|
_test_eve_cain()
|
|
#_test_eden()
|