# Copyright 2021 Facebook and Zilliz. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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# 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 torch
import math
from torch.optim import Optimizer
[docs]class Adafactor(Optimizer):
"""
AdaFactor pytorch implementation as introduced in `Adafactor: Adaptive Learning Rates with Sublinear Memory Cost`
https://arxiv.org/abs/1804.04235.
Args:
params (Iterable[nn.parameter.Parameter]):
Iterable of parameters to optimize or dictionaries defining parameter groups.
lr (float, optional):
The external learning rate.
eps (Tuple[float, float], optional):
Regularization constants for square gradient and parameter scale respectively.
clip_threshold (float, optional):
Threshold of root mean square of final gradient update.
decay_rate (float, optional):
Coefficient used to compute running averages of square.
beta1 (float, optional):
Coefficient used for computing running averages of gradient.
weight_decay (float, optional):
Weight decay (L2 penalty).
scale_parameter (bool, optional):
If True, learning rate is scaled by root mean square.
relative_step (bool, optional):
If True, time-dependent learning rate is computed instead of external learning rate.
warmup_init (bool, optional):
Time-dependent learning rate computation depends on whether warm-up initialization is being used.
"""
[docs] def __init__(
self,
params,
lr=None,
eps=(1e-30, 1e-3),
clip_threshold=1.0,
decay_rate=-0.8,
beta1=None,
weight_decay=0.0,
scale_parameter=True,
relative_step=True,
warmup_init=False,
):
if lr is not None and relative_step:
raise ValueError("Cannot combine manual `lr` and `relative_step=True` options")
if warmup_init and not relative_step:
raise ValueError("`warmup_init=True` requires `relative_step=True`")
defaults = dict(
lr=lr,
eps=eps,
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,
)
super().__init__(params, defaults)
@staticmethod
def _get_lr(param_group, param_state):
rel_step_sz = param_group["lr"]
if param_group["relative_step"]:
min_step = 1e-6 * param_state["step"] if param_group["warmup_init"] else 1e-2
rel_step_sz = 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"][1], param_state["RMS"])
return param_scale * rel_step_sz
@staticmethod
def _get_options(param_group, param_shape):
factored = len(param_shape) >= 2
use_first_moment = param_group["beta1"] is not None
return factored, use_first_moment
@staticmethod
def _rms(tensor):
return tensor.norm(2) / (tensor.numel() ** 0.5)
@staticmethod
def _approx_sq_grad(exp_avg_sq_row, exp_avg_sq_col):
r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=-1, keepdim=True)).rsqrt_()
c_factor = exp_avg_sq_col.rsqrt()
return torch.mm(r_factor.unsqueeze(-1), c_factor.unsqueeze(0))
[docs] def step(self, closure=None):
"""
Performs a single optimization step
Args:
closure(callable, optional): A closure that reevaluates the model and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group["params"]:
if p.grad is None:
continue
grad = p.grad.data
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]
grad_shape = grad.shape
factored, use_first_moment = self._get_options(group, grad_shape)
# 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:
state["exp_avg_sq_row"] = torch.zeros(grad_shape[:-1]).to(grad)
state["exp_avg_sq_col"] = torch.zeros(grad_shape[:-2] + grad_shape[-1:]).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:
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_data_fp32 = p.data
if p.data.dtype in {torch.float16, torch.bfloat16}:
p_data_fp32 = p_data_fp32.float()
state["step"] += 1
state["RMS"] = self._rms(p_data_fp32)
lr = self._get_lr(group, state)
beta2t = 1.0 - math.pow(state["step"], group["decay_rate"])
update = (grad ** 2) + group["eps"][0]
if factored:
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=-1), alpha=(1.0 - beta2t))
exp_avg_sq_col.mul_(beta2t).add_(update.mean(dim=-2), 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)
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)
if use_first_moment:
exp_avg = state["exp_avg"]
exp_avg.mul_(group["beta1"]).add_(update, alpha=(1 - group["beta1"]))
update = exp_avg
if group["weight_decay"] != 0:
p_data_fp32.add_(p_data_fp32, alpha=(-group["weight_decay"] * lr))
p_data_fp32.add_(-update)
if p.data.dtype in {torch.float16, torch.bfloat16}:
p.data.copy_(p_data_fp32)
return loss