""" 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