650 lines
26 KiB
Python
650 lines
26 KiB
Python
# mypy: allow-untyped-decorators
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# mypy: allow-untyped-defs
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r"""Implementation for the NAdam algorithm."""
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from typing import cast, List, Optional, Tuple, Union
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import torch
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from torch import Tensor
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from .optimizer import (
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_capturable_doc,
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_default_to_fused_or_foreach,
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_differentiable_doc,
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_disable_dynamo_if_unsupported,
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_foreach_doc,
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_get_capturable_supported_devices,
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_get_scalar_dtype,
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_get_value,
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_maximize_doc,
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_stack_if_compiling,
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_use_grad_for_differentiable,
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_view_as_real,
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Optimizer,
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ParamsT,
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)
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__all__ = ["NAdam", "nadam"]
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class NAdam(Optimizer): # noqa: D101
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def __init__(
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self,
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params: ParamsT,
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lr: Union[float, Tensor] = 2e-3,
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betas: Tuple[float, float] = (0.9, 0.999),
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eps: float = 1e-8,
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weight_decay: float = 0,
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momentum_decay: float = 4e-3,
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decoupled_weight_decay: bool = False,
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*,
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foreach: Optional[bool] = None,
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maximize: bool = False,
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capturable: bool = False,
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differentiable: bool = False,
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): # noqa: D107
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if isinstance(lr, Tensor) and lr.numel() != 1:
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raise ValueError("Tensor lr must be 1-element")
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if not 0.0 <= lr:
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raise ValueError(f"Invalid learning rate: {lr}")
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if not 0.0 <= eps:
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raise ValueError(f"Invalid epsilon value: {eps}")
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if not 0.0 <= betas[0] < 1.0:
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raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
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if not 0.0 <= betas[1] < 1.0:
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raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
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if not 0.0 <= weight_decay:
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raise ValueError(f"Invalid weight_decay value: {weight_decay}")
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if not 0.0 <= momentum_decay:
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raise ValueError(f"Invalid momentum_decay value: {momentum_decay}")
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defaults = dict(
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lr=lr,
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betas=betas,
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eps=eps,
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weight_decay=weight_decay,
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momentum_decay=momentum_decay,
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decoupled_weight_decay=decoupled_weight_decay,
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maximize=maximize,
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foreach=foreach,
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capturable=capturable,
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differentiable=differentiable,
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)
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super().__init__(params, defaults)
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def __setstate__(self, state): # noqa: D105
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super().__setstate__(state)
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for group in self.param_groups:
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group.setdefault("maximize", False)
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group.setdefault("foreach", None)
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group.setdefault("capturable", False)
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group.setdefault("differentiable", False)
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group.setdefault("decoupled_weight_decay", False)
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for p in group["params"]:
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p_state = self.state.get(p, [])
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if len(p_state) != 0:
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if not torch.is_tensor(p_state["step"]):
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step_val = float(p_state["step"])
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p_state["step"] = (
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torch.tensor(
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step_val, dtype=_get_scalar_dtype(), device=p.device
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)
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if group["capturable"]
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else torch.tensor(step_val, dtype=_get_scalar_dtype())
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)
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if not torch.is_tensor(p_state["mu_product"]):
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mu_prod_val = p_state["mu_product"]
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p_state["mu_product"] = (
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torch.tensor(
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mu_prod_val, dtype=_get_scalar_dtype(), device=p.device
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)
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if group["capturable"]
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else torch.tensor(mu_prod_val, dtype=_get_scalar_dtype())
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)
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def _init_group(
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self,
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group,
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params_with_grad,
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grads,
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exp_avgs,
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exp_avg_sqs,
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mu_products,
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state_steps,
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):
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has_complex = False
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for p in group["params"]:
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if p.grad is not None:
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has_complex |= torch.is_complex(p)
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params_with_grad.append(p)
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if p.grad.is_sparse:
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raise RuntimeError("NAdam does not support sparse gradients")
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grads.append(p.grad)
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state = self.state[p]
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# Lazy state initialization
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if len(state) == 0:
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# note(crcrpar): [special device hosting for step]
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# Deliberately host `step` and `mu_product` on CPU if capturable is False.
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# This is because kernel launches are costly on CUDA and XLA.
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state["step"] = (
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torch.zeros((), dtype=_get_scalar_dtype(), device=p.device)
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if group["capturable"]
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else torch.tensor(0.0, dtype=_get_scalar_dtype())
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)
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state["mu_product"] = (
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torch.ones((), dtype=_get_scalar_dtype(), device=p.device)
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if group["capturable"]
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else torch.tensor(1.0, dtype=_get_scalar_dtype())
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)
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# Exponential moving average of gradient values
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state["exp_avg"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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# Exponential moving average of squared gradient values
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state["exp_avg_sq"] = torch.zeros_like(
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p, memory_format=torch.preserve_format
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)
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exp_avgs.append(state["exp_avg"])
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exp_avg_sqs.append(state["exp_avg_sq"])
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mu_products.append(state["mu_product"])
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state_steps.append(state["step"])
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return has_complex
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@_use_grad_for_differentiable
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def step(self, closure=None):
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"""Perform a single optimization step.
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Args:
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closure (Callable, optional): A closure that reevaluates the model
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and returns the loss.
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"""
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self._cuda_graph_capture_health_check()
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loss = None
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if closure is not None:
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with torch.enable_grad():
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loss = closure()
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for group in self.param_groups:
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params_with_grad: List[Tensor] = []
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grads: List[Tensor] = []
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exp_avgs: List[Tensor] = []
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exp_avg_sqs: List[Tensor] = []
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mu_products: List[Tensor] = []
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state_steps: List[Tensor] = []
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beta1, beta2 = cast(Tuple[float, float], group["betas"])
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has_complex = self._init_group(
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group,
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params_with_grad,
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grads,
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exp_avgs,
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exp_avg_sqs,
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mu_products,
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state_steps,
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)
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nadam(
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params_with_grad,
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grads,
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exp_avgs,
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exp_avg_sqs,
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mu_products,
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state_steps,
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beta1=beta1,
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beta2=beta2,
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lr=group["lr"],
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weight_decay=group["weight_decay"],
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momentum_decay=group["momentum_decay"],
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eps=group["eps"],
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maximize=group["maximize"],
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decoupled_weight_decay=group["decoupled_weight_decay"],
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foreach=group["foreach"],
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capturable=group["capturable"],
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differentiable=group["differentiable"],
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has_complex=has_complex,
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)
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return loss
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NAdam.__doc__ = (
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r"""Implements NAdam algorithm.
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.. math::
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\begin{aligned}
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&\rule{110mm}{0.4pt} \\
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&\textbf{input} : \gamma_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)},
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\: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)} \\
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&\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)} \\
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&\hspace{13mm} \: \textit{decoupled\_weight\_decay}, \:\textit{maximize} \\
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&\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)},
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v_0 \leftarrow 0 \text{ ( second moment)} \\[-1.ex]
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&\rule{110mm}{0.4pt} \\
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&\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\
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&\hspace{5mm}\textbf{if} \: \textit{maximize}: \\
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&\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\
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&\hspace{5mm}\textbf{else} \\
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&\hspace{10mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\
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&\hspace{5mm} \theta_t \leftarrow \theta_{t-1} \\
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&\hspace{5mm} \textbf{if} \: \lambda \neq 0 \\
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&\hspace{10mm}\textbf{if} \: \textit{decoupled\_weight\_decay} \\
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&\hspace{15mm} \theta_t \leftarrow \theta_{t-1} - \gamma \lambda \theta_{t-1} \\
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&\hspace{10mm}\textbf{else} \\
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&\hspace{15mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\
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&\hspace{5mm} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{t \psi} \big) \\
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&\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\
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&\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\
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&\hspace{5mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\
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&\hspace{5mm}\widehat{m_t} \leftarrow \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex]
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& \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i}) \\
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&\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\
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&\hspace{5mm}\theta_t \leftarrow \theta_t - \gamma \widehat{m_t}/
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\big(\sqrt{\widehat{v_t}} + \epsilon \big) \\
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&\rule{110mm}{0.4pt} \\[-1.ex]
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&\bf{return} \: \theta_t \\[-1.ex]
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&\rule{110mm}{0.4pt} \\[-1.ex]
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\end{aligned}
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For further details regarding the algorithm we refer to `Incorporating Nesterov Momentum into Adam`_.
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"""
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+ rf"""
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Args:
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params (iterable): iterable of parameters to optimize or dicts defining
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parameter groups
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lr (float, Tensor, optional): learning rate (default: 2e-3)
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betas (Tuple[float, float], optional): coefficients used for computing
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running averages of gradient and its square (default: (0.9, 0.999))
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eps (float, optional): term added to the denominator to improve
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numerical stability (default: 1e-8)
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weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
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momentum_decay (float, optional): momentum momentum_decay (default: 4e-3)
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decoupled_weight_decay (bool, optional): whether to use decoupled weight
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decay as in AdamW to obtain NAdamW (default: False)
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{_foreach_doc}
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{_maximize_doc}
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{_capturable_doc}
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{_differentiable_doc}
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.. _Incorporating Nesterov Momentum into Adam:
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https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
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.. _Decoupled Weight Decay Regularization:
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https://arxiv.org/abs/1711.05101
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"""
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)
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def _single_tensor_nadam(
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params: List[Tensor],
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grads: List[Tensor],
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exp_avgs: List[Tensor],
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exp_avg_sqs: List[Tensor],
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mu_products: List[Tensor],
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state_steps: List[Tensor],
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*,
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beta1: float,
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beta2: float,
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lr: float,
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weight_decay: float,
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momentum_decay: float,
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eps: float,
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decoupled_weight_decay: bool,
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maximize: bool,
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capturable: bool,
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differentiable: bool,
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has_complex: bool,
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):
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for i, param in enumerate(params):
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grad = grads[i] if not maximize else -grads[i]
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exp_avg = exp_avgs[i]
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exp_avg_sq = exp_avg_sqs[i]
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mu_product = mu_products[i]
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step_t = state_steps[i]
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if torch.is_complex(param):
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param = torch.view_as_real(param)
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grad = torch.view_as_real(grad)
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exp_avg = torch.view_as_real(exp_avg)
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exp_avg_sq = torch.view_as_real(exp_avg_sq)
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# If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
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if not torch._utils.is_compiling() and capturable:
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capturable_supported_devices = _get_capturable_supported_devices()
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assert (
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param.device.type == mu_product.device.type == step_t.device.type
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and param.device.type in capturable_supported_devices
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), (
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f"If capturable=True, params, mu_products and state_steps must be "
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f"on supported devices: {capturable_supported_devices}."
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)
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# update step
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step_t += 1
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if capturable:
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step = step_t
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else:
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step = _get_value(step_t)
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bias_correction2 = 1 - beta2**step
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if weight_decay != 0:
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if decoupled_weight_decay:
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# Perform stepweight decay
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param.mul_(1 - lr * weight_decay)
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else:
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grad = grad.add(param, alpha=weight_decay)
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# calculate the momentum cache \mu^{t} and \mu^{t+1}
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mu = beta1 * (1.0 - 0.5 * (0.96 ** (step * momentum_decay)))
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mu_next = beta1 * (1.0 - 0.5 * (0.96 ** ((step + 1) * momentum_decay)))
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# update mu_product
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mu_product *= mu
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# decay the first and second moment running average coefficient
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exp_avg.lerp_(grad, 1 - beta1)
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exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
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denom = exp_avg_sq.div(bias_correction2).sqrt()
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if differentiable or capturable:
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denom = denom.add(eps)
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# Make autograd track the operations
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# by updating the grad and exp_avg directly and not using the
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# scalar "value" argument of addcdiv.
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mu_product_next = mu_product * mu_next
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grad = grad * (-lr * (1.0 - mu) / (1.0 - mu_product))
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exp_avg = exp_avg * (-lr * mu_next / (1.0 - mu_product_next))
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param.addcdiv_(grad, denom)
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param.addcdiv_(exp_avg, denom)
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else:
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mu_product_next = _get_value(mu_product) * mu_next
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denom.add_(eps)
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param.addcdiv_(
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grad, denom, value=(-lr * (1.0 - mu) / (1.0 - _get_value(mu_product)))
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)
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param.addcdiv_(
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exp_avg, denom, value=(-lr * mu_next) / (1.0 - mu_product_next)
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)
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def _multi_tensor_nadam(
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params: List[Tensor],
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grads: List[Tensor],
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exp_avgs: List[Tensor],
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exp_avg_sqs: List[Tensor],
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mu_products: List[Tensor],
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state_steps: List[Tensor],
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*,
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beta1: float,
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beta2: float,
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lr: float,
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weight_decay: float,
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momentum_decay: float,
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eps: float,
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decoupled_weight_decay: bool,
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maximize: bool,
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capturable: bool,
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differentiable: bool,
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has_complex: bool,
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):
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if len(params) == 0:
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return
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assert not differentiable, "_foreach ops don't support autograd"
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# If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
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if not torch._utils.is_compiling() and capturable:
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capturable_supported_devices = _get_capturable_supported_devices(
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supports_xla=False
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)
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assert all(
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p.device.type == mp.device.type == step.device.type
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and p.device.type in capturable_supported_devices
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for p, mp, step in zip(params, mu_products, state_steps)
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), f"If capturable=True, params, mu_products, and state_steps must be on supported devices: {capturable_supported_devices}."
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grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
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[params, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps] # type: ignore[list-item]
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)
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for (
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grouped_params_,
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grouped_grads_,
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grouped_exp_avgs_,
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grouped_exp_avg_sqs_,
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grouped_mu_products_,
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grouped_state_steps_,
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), _ in grouped_tensors.values():
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grouped_params = cast(List[Tensor], grouped_params_)
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grouped_grads = cast(List[Tensor], grouped_grads_)
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grouped_exp_avgs = cast(List[Tensor], grouped_exp_avgs_)
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grouped_exp_avg_sqs = cast(List[Tensor], grouped_exp_avg_sqs_)
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grouped_mu_products = cast(List[Tensor], grouped_mu_products_)
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grouped_state_steps = cast(List[Tensor], grouped_state_steps_)
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# handle complex
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if has_complex:
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_view_as_real(
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grouped_params, grouped_grads, grouped_exp_avgs, grouped_exp_avg_sqs
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)
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if maximize:
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grouped_grads = torch._foreach_neg(grouped_grads) # type: ignore[assignment]
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# Update steps
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# If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over
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# and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just
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# wrapped it once now. The alpha is required to assure we go to the right overload.
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if not torch._utils.is_compiling() and grouped_state_steps[0].is_cpu:
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torch._foreach_add_(
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grouped_state_steps, torch.tensor(1.0, device="cpu"), alpha=1.0
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)
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else:
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torch._foreach_add_(grouped_state_steps, 1)
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if weight_decay != 0:
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if decoupled_weight_decay:
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# Perform stepweight decay
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torch._foreach_mul_(grouped_params, 1 - lr * weight_decay)
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else:
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# Re-use the intermediate memory (grouped_grads) already allocated for maximize
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if maximize:
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torch._foreach_add_(
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grouped_grads, grouped_params, alpha=weight_decay
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)
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else:
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grouped_grads = torch._foreach_add( # type: ignore[assignment]
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grouped_grads, grouped_params, alpha=weight_decay
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)
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# Decay the first and second moment running average coefficient
|
|
torch._foreach_lerp_(grouped_exp_avgs, grouped_grads, 1 - beta1)
|
|
|
|
torch._foreach_mul_(grouped_exp_avg_sqs, beta2)
|
|
torch._foreach_addcmul_(
|
|
grouped_exp_avg_sqs, grouped_grads, grouped_grads, 1 - beta2
|
|
)
|
|
|
|
exp_avg_sq_sqrt = torch._foreach_sqrt(grouped_exp_avg_sqs)
|
|
|
|
bias_correction_sqrt: Union[Tuple[Tensor, ...], List[Tensor]]
|
|
mus: Union[Tuple[Tensor, ...], List[Tensor]]
|
|
mu_nexts: Union[Tuple[Tensor, ...], List[Tensor]]
|
|
if capturable:
|
|
# mus will be beta1 * (1 - 0.5 * 0.96 ** (step * momentum_decay))
|
|
exponent = torch._foreach_mul(grouped_state_steps, momentum_decay)
|
|
mus = torch._foreach_pow(0.96, exponent)
|
|
torch._foreach_mul_(mus, -0.5)
|
|
torch._foreach_add_(mus, 1.0)
|
|
torch._foreach_mul_(mus, beta1)
|
|
|
|
# mu_nexts will be beta1 * (1 - 0.5 * 0.96 ** ((step + 1) * momentum_decay))
|
|
torch._foreach_add_(exponent, momentum_decay)
|
|
mu_nexts = torch._foreach_pow(0.96, exponent)
|
|
torch._foreach_mul_(mu_nexts, -0.5)
|
|
torch._foreach_add_(mu_nexts, 1.0)
|
|
torch._foreach_mul_(mu_nexts, beta1)
|
|
|
|
# save peak memory as we don't need exponent anymore
|
|
del exponent
|
|
|
|
bias_correction_sqrt = torch._foreach_pow(beta2, grouped_state_steps)
|
|
# foreach_sub doesn't allow a scalar as the first arg
|
|
torch._foreach_sub_(bias_correction_sqrt, 1.0)
|
|
torch._foreach_neg_(bias_correction_sqrt)
|
|
torch._foreach_sqrt_(bias_correction_sqrt)
|
|
else:
|
|
bias_correction_sqrt = [
|
|
(1 - beta2 ** _get_value(step)) ** 0.5 for step in grouped_state_steps
|
|
]
|
|
mus = [
|
|
beta1 * (1.0 - 0.5 * (0.96 ** (_get_value(step) * momentum_decay)))
|
|
for step in grouped_state_steps
|
|
]
|
|
mu_nexts = [
|
|
beta1
|
|
* (1.0 - 0.5 * (0.96 ** ((_get_value(step) + 1) * momentum_decay)))
|
|
for step in grouped_state_steps
|
|
]
|
|
|
|
# update mu_products
|
|
torch._foreach_mul_(grouped_mu_products, mus)
|
|
|
|
torch._foreach_div_(exp_avg_sq_sqrt, bias_correction_sqrt)
|
|
torch._foreach_add_(exp_avg_sq_sqrt, eps)
|
|
|
|
# explicitly delete bias_correction refs to save memory
|
|
del bias_correction_sqrt
|
|
|
|
if capturable:
|
|
# Build up the step_size multiplier for grad, reusing mus' memory
|
|
torch._foreach_sub_(mus, 1.0)
|
|
torch._foreach_mul_(mus, lr)
|
|
# foreach_sub doesn't allow a scalar as the first arg
|
|
denom = torch._foreach_sub(grouped_mu_products, 1.0)
|
|
torch._foreach_neg_(denom)
|
|
torch._foreach_div_(mus, denom)
|
|
# - lr * (1 - mu) / (1 - mu_product)
|
|
step_size_grads = mus
|
|
# explicitly delete denom to save memory
|
|
del denom
|
|
|
|
# Build up the step_size multiplier for exp_avg, reusing mu_nexts' memory
|
|
denom = torch._foreach_mul(grouped_mu_products, mu_nexts)
|
|
torch._foreach_mul_(mu_nexts, lr)
|
|
# foreach_sub doesn't allow a scalar as the first arg, but it's okay because
|
|
# we need a negative here anyway
|
|
torch._foreach_sub_(denom, 1.0)
|
|
torch._foreach_div_(mu_nexts, denom)
|
|
# - lr * mu_next / (1 - mu_product * mu_next)
|
|
step_size_expavg = mu_nexts
|
|
# explicitly delete denom to save memory
|
|
del denom
|
|
|
|
# we cannot inplace into step_size_grads cuz it is a list of ScalarTensors
|
|
# and mul'ing with grouped_grads will result in a list of bigger Tensors
|
|
numerator = torch._foreach_mul(step_size_grads, grouped_grads)
|
|
torch._foreach_addcmul_(numerator, step_size_expavg, grouped_exp_avgs)
|
|
|
|
# finally, update params
|
|
torch._foreach_addcdiv_(grouped_params, numerator, exp_avg_sq_sqrt)
|
|
else:
|
|
step_size_grads = _stack_if_compiling(
|
|
[
|
|
(_get_value(lr) * (1.0 - mu) / (1.0 - _get_value(mu_product))) * -1
|
|
for mu_product, mu in zip(grouped_mu_products, mus)
|
|
]
|
|
)
|
|
step_size_expavg = _stack_if_compiling(
|
|
[
|
|
(
|
|
_get_value(lr)
|
|
* mu_next
|
|
/ (1.0 - _get_value(mu_product) * mu_next)
|
|
)
|
|
* -1
|
|
for mu_product, mu_next in zip(grouped_mu_products, mu_nexts)
|
|
]
|
|
)
|
|
|
|
torch._foreach_addcdiv_(
|
|
grouped_params, grouped_grads, exp_avg_sq_sqrt, step_size_grads # type: ignore[arg-type]
|
|
)
|
|
torch._foreach_addcdiv_(
|
|
grouped_params, grouped_exp_avgs, exp_avg_sq_sqrt, step_size_expavg # type: ignore[arg-type]
|
|
)
|
|
|
|
|
|
@_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_nadam)
|
|
def nadam(
|
|
params: List[Tensor],
|
|
grads: List[Tensor],
|
|
exp_avgs: List[Tensor],
|
|
exp_avg_sqs: List[Tensor],
|
|
mu_products: List[Tensor],
|
|
state_steps: List[Tensor],
|
|
# kwonly args with defaults are not supported by functions compiled with torchscript issue #70627
|
|
# setting this as kwarg for now as functional API is compiled by torch/distributed/optim
|
|
decoupled_weight_decay: bool = False,
|
|
foreach: Optional[bool] = None,
|
|
capturable: bool = False,
|
|
differentiable: bool = False,
|
|
has_complex: bool = False,
|
|
maximize: bool = False,
|
|
*,
|
|
beta1: float,
|
|
beta2: float,
|
|
lr: float,
|
|
weight_decay: float,
|
|
momentum_decay: float,
|
|
eps: float,
|
|
):
|
|
r"""Functional API that performs NAdam algorithm computation.
|
|
|
|
See :class:`~torch.optim.NAdam` for details.
|
|
"""
|
|
if not all(isinstance(t, torch.Tensor) for t in state_steps):
|
|
raise RuntimeError(
|
|
"API has changed, `state_steps` argument must contain a list of singleton tensors"
|
|
)
|
|
|
|
if not all(isinstance(t, torch.Tensor) for t in mu_products):
|
|
raise RuntimeError(
|
|
"API has changed, `mu_products` argument must contain a list of singleton tensors"
|
|
)
|
|
|
|
if foreach is None:
|
|
_, foreach = _default_to_fused_or_foreach(
|
|
params, differentiable, use_fused=False
|
|
)
|
|
|
|
if foreach and torch.jit.is_scripting():
|
|
raise RuntimeError("torch.jit.script not supported with foreach optimizers")
|
|
|
|
if foreach and not torch.jit.is_scripting():
|
|
func = _multi_tensor_nadam
|
|
else:
|
|
func = _single_tensor_nadam
|
|
|
|
func(
|
|
params,
|
|
grads,
|
|
exp_avgs,
|
|
exp_avg_sqs,
|
|
mu_products,
|
|
state_steps,
|
|
beta1=beta1,
|
|
beta2=beta2,
|
|
lr=lr,
|
|
weight_decay=weight_decay,
|
|
momentum_decay=momentum_decay,
|
|
maximize=maximize,
|
|
decoupled_weight_decay=decoupled_weight_decay,
|
|
eps=eps,
|
|
capturable=capturable,
|
|
differentiable=differentiable,
|
|
has_complex=has_complex,
|
|
)
|