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came.py
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came.py
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import math
import torch
import torch.optim
class CAME(torch.optim.Optimizer):
"""Implements CAME algorithm.
This implementation is based on:
`CAME: Confidence-guided Adaptive Memory Efficient Optimization`
Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): external learning rate (default: None)
eps (tuple[float, float]): regularization constants for square gradient
and instability respectively (default: (1e-30, 1e-16))
clip_threshold (float): threshold of root-mean-square of
final gradient update (default: 1.0)
betas (tuple[float, float, float]): coefficient used for computing running averages of
update, square gradient and instability (default: (0.9, 0.999, 0.9999)))
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
"""
def __init__(
self,
params,
lr=None,
eps=(1e-30, 1e-16),
clip_threshold=1.0,
betas=(0.9, 0.999, 0.9999),
weight_decay=0.0,
):
assert lr > 0.
assert all([0. <= beta <= 1. for beta in betas])
defaults = dict(
lr=lr,
eps=eps,
clip_threshold=clip_threshold,
betas=betas,
weight_decay=weight_decay,
)
super(CAME, self).__init__(params, defaults)
@property
def supports_memory_efficient_fp16(self):
return True
@property
def supports_flat_params(self):
return False
def _get_options(self, param_shape):
factored = len(param_shape) >= 2
return factored
def _rms(self, tensor):
return tensor.norm(2) / (tensor.numel() ** 0.5)
def _approx_sq_grad(self, exp_avg_sq_row, exp_avg_sq_col):
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.
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("CAME does not support sparse gradients.")
state = self.state[p]
grad_shape = grad.shape
factored = self._get_options(grad_shape)
# State Initialization
if len(state) == 0:
state["step"] = 0
state["exp_avg"] = torch.zeros_like(grad)
if factored:
state["exp_avg_sq_row"] = torch.zeros(grad_shape[:-1]).type_as(grad)
state["exp_avg_sq_col"] = torch.zeros(
grad_shape[:-2] + grad_shape[-1:]
).type_as(grad)
state["exp_avg_res_row"] = torch.zeros(grad_shape[:-1]).type_as(grad)
state["exp_avg_res_col"] = torch.zeros(
grad_shape[:-2] + grad_shape[-1:]
).type_as(grad)
else:
state["exp_avg_sq"] = torch.zeros_like(grad)
state["RMS"] = 0
state["step"] += 1
state["RMS"] = self._rms(p.data)
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_(group["betas"][1]).add_(
update.mean(dim=-1), alpha=1.0 - group["betas"][1]
)
exp_avg_sq_col.mul_(group["betas"][1]).add_(
update.mean(dim=-2), alpha=1.0 - group["betas"][1]
)
# 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_(group["betas"][1]).add_(update, alpha=1.0 - group["betas"][1])
update = exp_avg_sq.rsqrt().mul_(grad)
update.div_(
(self._rms(update) / group["clip_threshold"]).clamp_(min=1.0)
)
exp_avg = state["exp_avg"]
exp_avg.mul_(group["betas"][0]).add_(update, alpha=1 - group["betas"][0])
# Confidence-guided strategy
# Calculation of instability
res = (update - exp_avg)**2 + group["eps"][1]
if factored:
exp_avg_res_row = state["exp_avg_res_row"]
exp_avg_res_col = state["exp_avg_res_col"]
exp_avg_res_row.mul_(group["betas"][2]).add_(
res.mean(dim=-1), alpha=1.0 - group["betas"][2]
)
exp_avg_res_col.mul_(group["betas"][2]).add_(
res.mean(dim=-2), alpha=1.0 - group["betas"][2]
)
# Approximation of exponential moving average of instability
res_approx = self._approx_sq_grad(exp_avg_res_row, exp_avg_res_col)
update = res_approx.mul_(exp_avg)
else:
update = exp_avg
if group["weight_decay"] != 0:
p.data.add_(
p.data, alpha=-group["weight_decay"] * group["lr"]
)
update.mul_(group["lr"])
p.data.add_(-update)
return loss