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""" Adafactor Optimizer
Lifted from https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py
Modified by Ross Wightman to fix some issues with factorization dims for non nn.Linear layers
Original header/copyright below.
"""
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
import math
from typing import Optional, Tuple
import torch
from ._types import ParamsT
class Adafactor(torch.optim.Optimizer):
"""Implements Adafactor algorithm.
This implementation is based on: `Adafactor: Adaptive Learning Rates with Sublinear Memory Cost`
(see https://arxiv.org/abs/1804.04235)
Note that this optimizer internally adjusts the learning rate depending on the
*scale_parameter*, *relative_step* and *warmup_init* options.
To use a manual (external) learning rate schedule you should set `scale_parameter=False` and
`relative_step=False`.
Ags:
params: iterable of parameters to optimize or dicts defining parameter groups
lr: external learning rate
eps: regularization constants for square gradient and parameter scale respectively
eps_scale: regularization constants for parameter scale respectively
clip_threshold: threshold of root-mean-square of final gradient update
decay_rate: coefficient used to compute running averages of square gradient
beta1: coefficient used for computing running averages of gradient
weight_decay: weight decay
scale_parameter: if True, learning rate is scaled by root-mean-square of parameter
warmup_init: time-dependent learning rate computation depends on whether warm-up initialization is being used
"""
def __init__(
self,
params: ParamsT,
lr: Optional[float] = None,
eps: float = 1e-30,
eps_scale: float = 1e-3,
clip_threshold: float = 1.0,
decay_rate: float = -0.8,
betas: Optional[Tuple[float, float]] = None,
weight_decay: float = 0.0,
scale_parameter: bool = True,
warmup_init: bool = False,
min_dim_size_to_factor: int = 16,
caution: bool = False,
):
relative_step = not lr
if warmup_init and not relative_step:
raise ValueError('warmup_init requires relative_step=True')
beta1 = None if betas is None else betas[0] # make it compat with standard betas arg
defaults = dict(
lr=lr,
eps=eps,
eps_scale=eps_scale,
clip_threshold=clip_threshold,
decay_rate=decay_rate,
beta1=beta1,
weight_decay=weight_decay,
scale_parameter=scale_parameter,
relative_step=relative_step,
warmup_init=warmup_init,
min_dim_size_to_factor=min_dim_size_to_factor,
caution=caution,
)
super(Adafactor, self).__init__(params, defaults)
def __setstate__(self, state):
super().__setstate__(state)
for group in self.param_groups:
group.setdefault('caution', False)
group.setdefault('min_dim_size_to_factor', 16)
@staticmethod
def _get_lr(param_group, param_state):
if param_group['relative_step']:
min_step = 1e-6 * param_state['step'] if param_group['warmup_init'] else 1e-2
lr_t = min(min_step, 1.0 / math.sqrt(param_state['step']))
param_scale = 1.0
if param_group['scale_parameter']:
param_scale = max(param_group['eps_scale'], param_state['RMS'])
param_group['lr'] = lr_t * param_scale
return param_group['lr']
@staticmethod
def _get_options(param_group, param_shape, min_size_to_factor=16):
use_first_moment = param_group['beta1'] is not None
factored = None
ndim = len(param_shape)
# Use a simple heuristic to pick factorization row & col, note other PyTorch impl tend to
# always use -2, -1 BUT this will not pick correct dims for convolutions. This is a simple
# approach that should work in most cases, compare to the slightly more involved approach
# in AdafactorBigVision that sorts dims by size, please report if wrong dims chosen.
if ndim > 2 and param_shape[0] > min_size_to_factor and param_shape[1] > min_size_to_factor:
# nD convs in torch are ND + 2 dim weights with leading in/out chs
factored = 0, 1
elif ndim >= 2 and param_shape[-2] > min_size_to_factor and param_shape[-1] > min_size_to_factor:
# if the criteria above didn't match, test trailing dims for eligibility as per original impl
factored = ndim - 2, ndim - 1
return factored, use_first_moment
@staticmethod
def _rms(tensor):
return tensor.norm(2) / (tensor.numel() ** 0.5)
def _approx_sq_grad(self, exp_avg_sq_row, exp_avg_sq_col, dim_col, dim_row):
# from our dim heuristic, always dim_col < dim_row, so col reduction dim for factored row = dim_col
r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=dim_col, keepdim=True)).rsqrt_().unsqueeze(dim_row)
c_factor = exp_avg_sq_col.unsqueeze(dim_col).rsqrt()
return torch.mul(r_factor, c_factor)
@torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model and returns the loss.
"""
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad = p.grad
if grad.dtype in {torch.float16, torch.bfloat16}:
grad = grad.float()
if grad.is_sparse:
raise RuntimeError('Adafactor does not support sparse gradients.')
state = self.state[p]
factored_dims, use_first_moment = self._get_options(
group,
grad.shape,
min_size_to_factor=group['min_dim_size_to_factor'],
)
# State Initialization
if len(state) == 0:
state['step'] = 0
if use_first_moment:
# Exponential moving average of gradient values
state['exp_avg'] = torch.zeros_like(grad)
if factored_dims is not None:
dim_col, dim_row = factored_dims
def _remove_dim(shape, dim):
return shape[:dim] + shape[dim + 1:]
state['exp_avg_sq_row'] = torch.zeros(_remove_dim(grad.shape, dim_row)).to(grad)
state['exp_avg_sq_col'] = torch.zeros(_remove_dim(grad.shape, dim_col)).to(grad)
else:
state['exp_avg_sq'] = torch.zeros_like(grad)
state['RMS'] = 0
else:
if use_first_moment:
state['exp_avg'] = state['exp_avg'].to(grad)
if factored_dims is not None:
state['exp_avg_sq_row'] = state['exp_avg_sq_row'].to(grad)
state['exp_avg_sq_col'] = state['exp_avg_sq_col'].to(grad)
else:
state['exp_avg_sq'] = state['exp_avg_sq'].to(grad)
p_fp32 = p
if p.dtype in {torch.float16, torch.bfloat16}:
p_fp32 = p_fp32.float()
state['step'] += 1
state['RMS'] = self._rms(p_fp32)
lr_t = self._get_lr(group, state)
beta2t = 1.0 - math.pow(state['step'], group['decay_rate'])
update = grad ** 2 + group['eps']
if factored_dims is not None:
dim_col, dim_row = factored_dims
exp_avg_sq_row = state['exp_avg_sq_row']
exp_avg_sq_col = state['exp_avg_sq_col']
exp_avg_sq_row.mul_(beta2t).add_(update.mean(dim=dim_row), alpha=1.0 - beta2t)
exp_avg_sq_col.mul_(beta2t).add_(update.mean(dim=dim_col), alpha=1.0 - beta2t)
# Approximation of exponential moving average of square of gradient
update = self._approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col, dim_col, dim_row)
update.mul_(grad)
else:
exp_avg_sq = state['exp_avg_sq']
exp_avg_sq.mul_(beta2t).add_(update, alpha=1.0 - beta2t)
update = exp_avg_sq.rsqrt().mul_(grad)
update.div_((self._rms(update) / group['clip_threshold']).clamp_(min=1.0))
update.mul_(lr_t)
if use_first_moment:
exp_avg = state['exp_avg']
exp_avg.mul_(group['beta1']).add_(update, alpha=1 - group['beta1'])
if group['caution']:
# Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085
mask = (exp_avg * grad > 0).to(grad.dtype)
mask.div_(mask.mean().clamp_(min=1e-3))
update = exp_avg * mask
else:
update = exp_avg
if group['weight_decay'] != 0:
p_fp32.add_(p_fp32, alpha=-group['weight_decay'] * lr_t)
p_fp32.add_(-update)
if p.dtype in {torch.float16, torch.bfloat16}:
p.copy_(p_fp32)
return loss
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