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import math
import torch
from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR
__all__ = ['Adafactor']
class Adafactor(Optimizer):
"""
AdaFactor pytorch implementation can be used as a drop in replacement for Adam original fairseq code:
https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py
Paper: *Adafactor: Adaptive Learning Rates with Sublinear Memory Cost* 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`.
Arguments:
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*, defaults to (1e-30, 1e-3)):
Regularization constants for square gradient and parameter scale respectively
clip_threshold (`float`, *optional*, defaults 1.0):
Threshold of root mean square of final gradient update
decay_rate (`float`, *optional*, defaults to -0.8):
Coefficient used to compute running averages of square
beta1 (`float`, *optional*):
Coefficient used for computing running averages of gradient
weight_decay (`float`, *optional*, defaults to 0):
Weight decay (L2 penalty)
scale_parameter (`bool`, *optional*, defaults to `True`):
If True, learning rate is scaled by root mean square
relative_step (`bool`, *optional*, defaults to `True`):
If True, time-dependent learning rate is computed instead of external learning rate
warmup_init (`bool`, *optional*, defaults to `False`):
Time-dependent learning rate computation depends on whether warm-up initialization is being used
This implementation handles low-precision (FP16, bfloat) values, but we have not thoroughly tested.
Recommended T5 finetuning settings (https://discuss.huggingface.co/t/t5-finetuning-tips/684/3):
- Training without LR warmup or clip_threshold is not recommended.
- use scheduled LR warm-up to fixed LR
- use clip_threshold=1.0 (https://arxiv.org/abs/1804.04235)
- Disable relative updates
- Use scale_parameter=False
- Additional optimizer operations like gradient clipping should not be used alongside Adafactor
Example:
```python
Adafactor(model.parameters(), scale_parameter=False, relative_step=False, warmup_init=False, lr=1e-3)
```
Others reported the following combination to work well:
```python
Adafactor(model.parameters(), scale_parameter=True, relative_step=True, warmup_init=True, lr=None)
```
When using `lr=None` with [`Trainer`] you will most likely need to use [`~optimization.AdafactorSchedule`]
scheduler as following:
```python
from transformers.optimization import Adafactor, AdafactorSchedule
optimizer = Adafactor(model.parameters(), scale_parameter=True, relative_step=True, warmup_init=True, lr=None)
lr_scheduler = AdafactorSchedule(optimizer)
trainer = Trainer(..., optimizers=(optimizer, lr_scheduler))
```
Usage:
```python
# replace AdamW with Adafactor
optimizer = Adafactor(
model.parameters(),
lr=1e-3,
eps=(1e-30, 1e-3),
clip_threshold=1.0,
decay_rate=-0.8,
beta1=None,
weight_decay=0.0,
relative_step=False,
scale_parameter=False,
warmup_init=False,
)
```"""
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,
):
r"""require_version("torch>=1.5.0") # add_ with alpha
"""
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):
# copy from fairseq's adafactor implementation:
# https://github.com/huggingface/transformers/blob/8395f14de6068012787d83989c3627c3df6a252b/src/transformers/optimization.py#L505
r_factor = (exp_avg_sq_row / exp_avg_sq_row.mean(dim=-1, keepdim=True)).rsqrt_().unsqueeze(-1)
c_factor = exp_avg_sq_col.unsqueeze(-2).rsqrt()
return torch.mul(r_factor, c_factor)
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:
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
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