image-match/python/py/Lib/site-packages/torch/optim/adam.py

# mypy: allow-untyped-defs
from typing import cast

import torch
from torch import Tensor

from .optimizer import (
    _capturable_doc,
    _default_to_fused_or_foreach,
    _device_dtype_check_for_fused,
    _differentiable_doc,
    _disable_dynamo_if_unsupported,
    _foreach_doc,
    _fused_doc,
    _get_capturable_supported_devices,
    _get_scalar_dtype,
    _get_value,
    _maximize_doc,
    _params_doc,
    _stack_if_compiling,
    _to_scalar,
    _use_grad_for_differentiable,
    _view_as_real,
    DeviceDict,
    DeviceDtypeDict,
    Optimizer,
    ParamsT,
)


__all__ = ["Adam", "adam"]


class Adam(Optimizer):
    def __init__(
        self,
        params: ParamsT,
        lr: float | Tensor = 1e-3,
        betas: tuple[float | Tensor, float | Tensor] = (0.9, 0.999),
        eps: float = 1e-8,
        weight_decay: float = 0,
        amsgrad: bool = False,
        *,
        foreach: bool | None = None,
        maximize: bool = False,
        capturable: bool = False,
        differentiable: bool = False,
        fused: bool | None = None,
        decoupled_weight_decay: bool = False,
    ) -> None:
        if isinstance(lr, Tensor):
            if foreach and not capturable:
                raise ValueError(
                    "lr as a Tensor is not supported for capturable=False and foreach=True"
                )
            if lr.numel() != 1:
                raise ValueError("Tensor lr must be 1-element")
        if not 0.0 <= lr:
            raise ValueError(f"Invalid learning rate: {lr}")
        if not 0.0 <= eps:
            raise ValueError(f"Invalid epsilon value: {eps}")
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
        if not 0.0 <= weight_decay:
            raise ValueError(f"Invalid weight_decay value: {weight_decay}")
        if not (
            (isinstance(betas[0], float) and isinstance(betas[1], float))
            or (isinstance(betas[0], Tensor) and isinstance(betas[1], Tensor))
        ):
            raise ValueError("betas must be either both floats or both Tensors")
        if isinstance(betas[0], Tensor):
            if not capturable and foreach:
                raise ValueError(
                    "betas[0] as a Tensor is not supported for capturable=False and foreach=True"
                )
            if betas[0].numel() != 1:
                raise ValueError("Tensor betas[0] must be 1-element")
        if isinstance(betas[1], Tensor):
            if not capturable and foreach:
                raise ValueError(
                    "betas[1] as a Tensor is not supported for capturable=False and foreach=True"
                )
            if betas[1].numel() != 1:
                raise ValueError("Tensor betas[1] must be 1-element")
        betas = tuple(map(_to_scalar, betas))

        defaults = {
            "lr": lr,
            "betas": betas,
            "eps": eps,
            "weight_decay": weight_decay,
            "amsgrad": amsgrad,
            "maximize": maximize,
            "foreach": foreach,
            "capturable": capturable,
            "differentiable": differentiable,
            "fused": fused,
            "decoupled_weight_decay": decoupled_weight_decay,
        }
        super().__init__(params, defaults)

        if fused:
            if differentiable:
                raise RuntimeError("`fused` does not support `differentiable`")
            self._step_supports_amp_scaling = True
            # TODO(crcrpar): [low prec params & their higher prec copy]
            # Support AMP with FP16/BF16 model params which would need
            # higher prec copy of params to do update math in higher prec to
            # alleviate the loss of information.
            if foreach:
                raise RuntimeError("`fused` and `foreach` cannot be `True` together.")

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault("amsgrad", False)
            group.setdefault("maximize", False)
            group.setdefault("foreach", None)
            group.setdefault("capturable", False)
            group.setdefault("differentiable", False)
            group.setdefault("decoupled_weight_decay", False)
            fused = group.setdefault("fused", None)
            for p in group["params"]:
                p_state = self.state.get(p, [])
                if len(p_state) != 0 and not torch.is_tensor(p_state["step"]):
                    step_val = float(p_state["step"])
                    p_state["step"] = (
                        torch.tensor(
                            step_val,
                            dtype=_get_scalar_dtype(is_fused=fused),
                            device=p.device,
                        )
                        if group["capturable"] or group["fused"]
                        else torch.tensor(step_val, dtype=_get_scalar_dtype())
                    )

    def _init_group(
        self,
        group,
        params_with_grad,
        grads,
        exp_avgs,
        exp_avg_sqs,
        max_exp_avg_sqs,
        state_steps,
    ):
        has_complex = False
        for p in group["params"]:
            if p.grad is not None:
                has_complex |= torch.is_complex(p)
                params_with_grad.append(p)
                if p.grad.is_sparse:
                    raise RuntimeError(
                        "Adam does not support sparse gradients, please consider SparseAdam instead"
                    )
                grads.append(p.grad)

                state = self.state[p]
                # Lazy state initialization
                if len(state) == 0:
                    if group["fused"]:
                        _device_dtype_check_for_fused(p)
                    # note(crcrpar): [special device hosting for step]
                    # Deliberately host `step` on CPU if both capturable and fused are off.
                    # This is because kernel launches are costly on CUDA and XLA.
                    state["step"] = (
                        torch.zeros(
                            (),
                            dtype=_get_scalar_dtype(is_fused=group["fused"]),
                            device=p.device,
                        )
                        if group["capturable"] or group["fused"]
                        else torch.tensor(0.0, dtype=_get_scalar_dtype())
                    )
                    # Exponential moving average of gradient values
                    state["exp_avg"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
                    # Exponential moving average of squared gradient values
                    state["exp_avg_sq"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
                    if group["amsgrad"]:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state["max_exp_avg_sq"] = torch.zeros_like(
                            p, memory_format=torch.preserve_format
                        )

                exp_avgs.append(state["exp_avg"])
                exp_avg_sqs.append(state["exp_avg_sq"])

                if group["amsgrad"]:
                    max_exp_avg_sqs.append(state["max_exp_avg_sq"])
                if group["differentiable"] and state["step"].requires_grad:
                    raise RuntimeError(
                        "`requires_grad` is not supported for `step` in differentiable mode"
                    )

                # Foreach without capturable does not support a tensor lr
                if (
                    group["foreach"]
                    and torch.is_tensor(group["lr"])
                    and not group["capturable"]
                ):
                    raise RuntimeError(
                        "lr as a Tensor is not supported for capturable=False and foreach=True"
                    )

                state_steps.append(state["step"])
        return has_complex

    @_use_grad_for_differentiable
    def step(self, closure=None):
        """Perform a single optimization step.

        Args:
            closure (Callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        self._accelerator_graph_capture_health_check()

        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad: list[Tensor] = []
            grads: list[Tensor] = []
            exp_avgs: list[Tensor] = []
            exp_avg_sqs: list[Tensor] = []
            max_exp_avg_sqs: list[Tensor] = []
            state_steps: list[Tensor] = []
            beta1, beta2 = group["betas"]

            has_complex = self._init_group(
                group,
                params_with_grad,
                grads,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps,
            )

            adam(
                params_with_grad,
                grads,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps,
                amsgrad=group["amsgrad"],
                has_complex=has_complex,
                beta1=beta1,
                beta2=beta2,
                lr=group["lr"],
                weight_decay=group["weight_decay"],
                eps=group["eps"],
                maximize=group["maximize"],
                foreach=group["foreach"],
                capturable=group["capturable"],
                differentiable=group["differentiable"],
                fused=group["fused"],
                grad_scale=getattr(self, "grad_scale", None),
                found_inf=getattr(self, "found_inf", None),
                decoupled_weight_decay=group["decoupled_weight_decay"],
            )

        return loss


Adam.__doc__ = (
    r"""Implements Adam algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma \text{ (lr)}, \beta_1, \beta_2
                \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)}          \\
            &\hspace{13mm}      \lambda \text{ (weight decay)},  \: \textit{amsgrad},
                \:\textit{maximize},  \: \epsilon \text{ (epsilon)}                              \\
            &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                v_0\leftarrow 0 \text{ (second moment)},\: v_0^{max}\leftarrow 0          \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\

            &\hspace{5mm}\textbf{if} \: \textit{maximize}:                                       \\
            &\hspace{10mm}g_t           \leftarrow   -\nabla_{\theta} f_t (\theta_{t-1})         \\
            &\hspace{5mm}\textbf{else}                                                           \\
            &\hspace{10mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})          \\
            &\hspace{5mm}\textbf{if} \: \lambda \neq 0                                           \\
            &\hspace{10mm} g_t \leftarrow g_t + \lambda  \theta_{t-1}                            \\
            &\hspace{5mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
            &\hspace{5mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
            &\hspace{5mm}\widehat{m_t} \leftarrow   m_t/\big(1-\beta_1^t \big)                   \\
            &\hspace{5mm}\textbf{if} \: amsgrad                                                  \\
            &\hspace{10mm} v_t^{max} \leftarrow \mathrm{max}(v_{t-1}^{max},v_t)                  \\
            &\hspace{10mm}\widehat{v_t} \leftarrow v_t^{max}/\big(1-\beta_2^t \big)              \\
            &\hspace{5mm}\textbf{else}                                                           \\
            &\hspace{10mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                  \\
            &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
                \big(\sqrt{\widehat{v_t}} + \epsilon \big)                                       \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to `Adam: A Method for Stochastic Optimization`_.
    """
    + rf"""
    Args:
        {_params_doc}
        lr (float, Tensor, optional): learning rate (default: 1e-3). A tensor LR
            is not yet supported for all our implementations. Please use a float
            LR if you are not also specifying fused=True or capturable=True.
        betas (tuple[Union[float, Tensor], Union[float, Tensor]], optional):
            coefficients used for computing running averages of gradient and
            its square. If a tensor is provided, must be 1-element. (default: (0.9, 0.999))
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        decoupled_weight_decay (bool, optional): if True, this optimizer is
            equivalent to AdamW and the algorithm will not accumulate weight
            decay in the momentum nor variance. (default: False)
        amsgrad (bool, optional): whether to use the AMSGrad variant of this
            algorithm from the paper `On the Convergence of Adam and Beyond`_
            (default: False)
        {_foreach_doc}
        {_maximize_doc}
        {_capturable_doc}
        {_differentiable_doc}
        {_fused_doc}
    .. Note::
        A prototype implementation of Adam and AdamW for MPS supports `torch.float32` and `torch.float16`.
    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    .. _On the Convergence of Adam and Beyond:
        https://openreview.net/forum?id=ryQu7f-RZ

    """
)


def _single_tensor_adam(
    params: list[Tensor],
    grads: list[Tensor],
    exp_avgs: list[Tensor],
    exp_avg_sqs: list[Tensor],
    max_exp_avg_sqs: list[Tensor],
    state_steps: list[Tensor],
    grad_scale: Tensor | None,
    found_inf: Tensor | None,
    *,
    amsgrad: bool,
    has_complex: bool,
    beta1: float | Tensor,
    beta2: float | Tensor,
    lr: float | Tensor,
    weight_decay: float,
    eps: float,
    maximize: bool,
    capturable: bool,
    differentiable: bool,
    decoupled_weight_decay: bool,
) -> None:
    if grad_scale is not None or found_inf is not None:
        raise AssertionError("Expected grad_scale and found_inf to be None")

    if torch.jit.is_scripting():
        # this assert is due to JIT being dumb and not realizing that the ops below
        # have overloads to handle both float and Tensor lrs, so we just assert it's
        # a float since most people using JIT are using floats
        if not isinstance(lr, float):
            raise AssertionError(f"Expected lr to be a float, but got {type(lr)}")
        if not isinstance(beta1, float):
            raise AssertionError(f"Expected beta1 to be a float, but got {type(beta1)}")
        if not isinstance(beta2, float):
            raise AssertionError(f"Expected beta2 to be a float, but got {type(beta2)}")
    else:
        lr = _to_scalar(lr)
        beta1 = _to_scalar(beta1)
        beta2 = _to_scalar(beta2)

    # We only shuffle around the beta when it is a Tensor, otherwise, we prefer
    # treating it as a scalar.
    # Note: ensure type declaration is under conditional check for isinstance
    # or else torchscript will get cranky about the DeviceDict type.
    if isinstance(beta1, Tensor):
        beta1_dict: DeviceDtypeDict | None = {(beta1.device, beta1.dtype): beta1}
    else:
        beta1_dict = None

    for i, param in enumerate(params):
        grad = grads[i] if not maximize else -grads[i]
        exp_avg = exp_avgs[i]
        exp_avg_sq = exp_avg_sqs[i]
        step_t = state_steps[i]

        # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
        if not torch.compiler.is_compiling() and capturable:
            capturable_supported_devices = _get_capturable_supported_devices()
            if not (
                param.device.type == step_t.device.type
                and param.device.type in capturable_supported_devices
            ):
                raise AssertionError(
                    f"If capturable=True, params and state_steps must be on supported devices: {capturable_supported_devices}."
                )

        # update step
        step_t += 1

        if weight_decay != 0:
            if decoupled_weight_decay:
                # Perform stepweight decay
                param.mul_(1 - lr * weight_decay)
            else:
                # Nested if is necessary to bypass jitscript rules
                if differentiable and isinstance(weight_decay, Tensor):
                    if weight_decay.requires_grad:
                        grad = grad.addcmul_(param.clone(), weight_decay)
                    else:
                        # pyrefly: ignore [bad-argument-type]
                        grad = grad.add(param, alpha=weight_decay)
                else:
                    grad = grad.add(param, alpha=weight_decay)

        if torch.is_complex(param):
            grad = torch.view_as_real(grad)
            exp_avg = torch.view_as_real(exp_avg)
            exp_avg_sq = torch.view_as_real(exp_avg_sq)
            if amsgrad:
                max_exp_avg_sqs[i] = torch.view_as_real(max_exp_avg_sqs[i])
            param = torch.view_as_real(param)

        device = param.device

        if beta1_dict is not None:
            dtype = param.dtype  # type: ignore[union-attr]

            # cast to workaround https://github.com/pytorch/pytorch/issues/140601
            key = (device, dtype)
            if key not in beta1_dict:
                beta1_dict[key] = beta1.to(  # type: ignore[union-attr]
                    device=device, dtype=dtype, non_blocking=True
                )

            device_beta1: float | Tensor = beta1_dict[key]
        else:
            device_beta1 = beta1

        # Decay the first and second moment running average coefficient

        exp_avg.lerp_(grad, 1 - device_beta1)

        # Nested if is necessary to bypass jitscript rules
        if differentiable and isinstance(beta2, Tensor):
            if beta2.requires_grad:
                # Using lerp to only use 2 operations bc addcmul's value cannot be a tensor
                # Showing equivalence of differentiable path and nondifferentiable path
                # expavg * b2 + grad^2 * (1-b2)
                #           add expavg * (1-b2) - expavg * (1-b2) = 0
                # expavg * b2 + expavg * (1-b2) - expavg * (1-b2) + grad^2 * (1-b2)
                # expavg - expavg * (1-b2) + grad^2 * (1-b2)
                # expavg + (grad^2 - expavg) * (1-b2)
                # expavg.lerp(grad^2, 1-beta2)
                exp_avg_sq.lerp_(torch.square(grad), weight=1 - beta2)
            else:
                exp_avg_sq.mul_(beta2).addcmul_(
                    grad, grad, value=cast(float, 1 - beta2)
                )
        else:
            exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)  # type: ignore[arg-type]

        if capturable or differentiable:
            step = step_t

            # Nested if is necessary to bypass jitscript rules
            if differentiable and isinstance(beta1, Tensor):
                if beta1.requires_grad:
                    bias_correction1 = 1 - beta1 ** step.clone()
                else:
                    bias_correction1 = 1 - beta1**step
            else:
                bias_correction1 = 1 - beta1**step

            # Nested if is necessary to bypass jitscript rules
            if differentiable and isinstance(beta2, Tensor):
                if beta2.requires_grad:
                    bias_correction2 = 1 - beta2 ** step.clone()
                else:
                    bias_correction2 = 1 - beta2**step
            else:
                bias_correction2 = 1 - beta2**step

            step_size = lr / bias_correction1
            step_size_neg = step_size.neg()

            bias_correction2_sqrt = bias_correction2.sqrt()

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                if differentiable:
                    max_exp_avg_sq = max_exp_avg_sqs[i].clone()
                else:
                    max_exp_avg_sq = max_exp_avg_sqs[i]

                max_exp_avg_sqs[i].copy_(torch.maximum(max_exp_avg_sq, exp_avg_sq))

                # Uses the max. for normalizing running avg. of gradient
                # Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write
                # (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor)
                denom = (
                    max_exp_avg_sqs[i].sqrt() / (bias_correction2_sqrt * step_size_neg)
                ).add_(eps / step_size_neg)
            else:
                denom = (
                    exp_avg_sq.sqrt() / (bias_correction2_sqrt * step_size_neg)
                ).add_(eps / step_size_neg)

            if differentiable:
                param.addcdiv_(exp_avg.clone(), denom)
            else:
                param.addcdiv_(exp_avg, denom)
        else:
            step = _get_value(step_t)

            bias_correction1 = 1 - beta1**step
            bias_correction2 = 1 - beta2**step

            step_size = lr / bias_correction1

            bias_correction2_sqrt = bias_correction2**0.5

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch.maximum(max_exp_avg_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i])

                # Use the max. for normalizing running avg. of gradient
                denom = (max_exp_avg_sqs[i].sqrt() / bias_correction2_sqrt).add_(eps)
            else:
                denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps)

            param.addcdiv_(exp_avg, denom, value=-step_size)  # type: ignore[arg-type]

        # Lastly, switch back to complex view
        if amsgrad and torch.is_complex(params[i]):
            max_exp_avg_sqs[i] = torch.view_as_complex(max_exp_avg_sqs[i])


def _multi_tensor_adam(
    params: list[Tensor],
    grads: list[Tensor],
    exp_avgs: list[Tensor],
    exp_avg_sqs: list[Tensor],
    max_exp_avg_sqs: list[Tensor],
    state_steps: list[Tensor],
    grad_scale: Tensor | None,
    found_inf: Tensor | None,
    *,
    amsgrad: bool,
    has_complex: bool,
    beta1: float | Tensor,
    beta2: float | Tensor,
    lr: float | Tensor,
    weight_decay: float,
    eps: float,
    maximize: bool,
    capturable: bool,
    differentiable: bool,
    decoupled_weight_decay: bool,
) -> None:
    if len(params) == 0:
        return

    if isinstance(lr, Tensor):
        if not capturable:
            raise RuntimeError(
                "lr as a Tensor is not supported for capturable=False and foreach=True"
            )
        if lr.numel() != 1:
            raise ValueError("Tensor lr must be 1-element")

    if isinstance(beta1, Tensor):
        if not capturable:
            raise ValueError(
                "beta1 as a Tensor is not supported for capturable=False and foreach=True"
            )
        if beta1.numel() != 1:
            raise ValueError("Tensor beta1 must be 1-element")

    if isinstance(beta2, Tensor):
        if not capturable:
            raise ValueError(
                "beta2 as a Tensor is not supported for capturable=False and foreach=True"
            )
        if beta2.numel() != 1:
            raise ValueError("Tensor beta2 must be 1-element")

    # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
    if not torch.compiler.is_compiling() and capturable:
        capturable_supported_devices = _get_capturable_supported_devices(
            supports_xla=False
        )
        if not all(
            p.device.type == step.device.type
            and p.device.type in capturable_supported_devices
            for p, step in zip(params, state_steps, strict=True)
        ):
            raise AssertionError(
                f"If capturable=True, params and state_steps must be on supported devices: {capturable_supported_devices}."
            )

    if grad_scale is not None or found_inf is not None:
        raise AssertionError("Expected grad_scale and found_inf to be None")

    if differentiable:
        raise AssertionError("_foreach ops don't support autograd")

    lr = _to_scalar(lr)
    beta1 = _to_scalar(beta1)
    beta2 = _to_scalar(beta2)

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
        [params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps]  # type: ignore[list-item]
    )

    # We only shuffle around the beta when it is a Tensor and on CUDA, otherwise, we prefer
    # treating it as a scalar.
    beta1_dict: DeviceDict | None = (  # type: ignore[attr-defined]
        {beta1.device: beta1}
        if isinstance(beta1, Tensor) and str(beta1.device) != "cpu"
        else None
    )

    for (
        device_params_,
        device_grads_,
        device_exp_avgs_,
        device_exp_avg_sqs_,
        device_max_exp_avg_sqs_,
        device_state_steps_,
    ), _ in grouped_tensors.values():
        device_params = cast(list[Tensor], device_params_)
        device_grads = cast(list[Tensor], device_grads_)
        device_exp_avgs = cast(list[Tensor], device_exp_avgs_)
        device_exp_avg_sqs = cast(list[Tensor], device_exp_avg_sqs_)
        device_state_steps = cast(list[Tensor], device_state_steps_)

        device = device_params[0].device
        if beta1_dict is not None and device not in beta1_dict:
            beta1_dict[device] = beta1.to(device=device, non_blocking=True)  # type: ignore[union-attr, attr-defined]

        device_beta1 = beta1_dict[device] if beta1_dict else beta1

        # Handle complex parameters
        if has_complex:
            if amsgrad:
                device_max_exp_avg_sqs = cast(list[Tensor], device_max_exp_avg_sqs_)
                _view_as_real(
                    device_params,
                    device_grads,
                    device_exp_avgs,
                    device_exp_avg_sqs,
                    device_max_exp_avg_sqs,
                )
            else:
                _view_as_real(
                    device_params, device_grads, device_exp_avgs, device_exp_avg_sqs
                )

        if maximize:
            device_grads = torch._foreach_neg(device_grads)  # type: ignore[assignment]

        # Update steps
        # If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over
        # and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just
        # wrapped it once now. The alpha is required to assure we go to the right overload.
        if not torch.compiler.is_compiling() and device_state_steps[0].is_cpu:
            torch._foreach_add_(
                device_state_steps, torch.tensor(1.0, device="cpu"), alpha=1.0
            )
        else:
            torch._foreach_add_(device_state_steps, 1)

        if weight_decay != 0:
            if decoupled_weight_decay:
                # Perform stepweight decay
                torch._foreach_mul_(device_params, 1 - lr * weight_decay)
            else:
                # Reuse the intermediate memory (device_grads) already allocated for maximize
                if maximize:
                    torch._foreach_add_(device_grads, device_params, alpha=weight_decay)
                else:
                    device_grads = torch._foreach_add(  # type: ignore[assignment]
                        device_grads, device_params, alpha=weight_decay
                    )

        # Decay the first and second moment running average coefficient
        # Use device beta1 if beta1 is a tensor to ensure all
        # tensors are on the same device
        torch._foreach_lerp_(
            device_exp_avgs, device_grads, cast(float, 1 - device_beta1)
        )

        torch._foreach_mul_(device_exp_avg_sqs, beta2)

        # Due to the strictness of the _foreach_addcmul API, we can't have a single
        # tensor scalar as the scalar arg (only python number is supported there)
        # as a result, separate out the value mul
        # Filed https://github.com/pytorch/pytorch/issues/139795
        if isinstance(beta2, torch.Tensor):
            scaled_device_grads = torch._foreach_mul(device_grads, 1 - beta2)  # type: ignore[assignment]
            value = 1.0
        else:
            scaled_device_grads = device_grads  # type: ignore[assignment]
            value = 1 - beta2

        torch._foreach_addcmul_(
            device_exp_avg_sqs, scaled_device_grads, device_grads, value
        )

        # Delete the local intermediate(s) since they won't be used anymore to save on peak memory
        del device_grads
        del scaled_device_grads

        bias_correction1: tuple[Tensor, ...] | list[Tensor]
        bias_correction2: tuple[Tensor, ...] | list[Tensor]
        bias_correction2_sqrt: tuple[Tensor, ...] | list[Tensor]

        if capturable:
            bias_correction1 = torch._foreach_pow(beta1, device_state_steps)  # type: ignore[arg-type]
            bias_correction2 = torch._foreach_pow(beta2, device_state_steps)  # type: ignore[arg-type]
            # foreach_sub doesn't allow a scalar as the first arg
            torch._foreach_sub_(bias_correction1, 1)
            torch._foreach_sub_(bias_correction2, 1)
            # we do not negate bias_correction1 as it'll need to be negated later anyway
            torch._foreach_neg_(bias_correction2)

            # foreach_div doesn't allow a scalar as the first arg
            torch._foreach_div_(bias_correction1, lr)
            torch._foreach_reciprocal_(bias_correction1)

            torch._foreach_sqrt_(bias_correction2)

            # Re-assign for clarity as we maintain minimal intermediates: we'll have
            # step_size = - lr / (1 - beta1 ^ t) where t = num_steps
            # bias_correction2_sqrt = sqrt(1 - beta2 ^ t)
            step_size = bias_correction1
            bias_correction2_sqrt = bias_correction2

            if amsgrad:
                device_max_exp_avg_sqs = cast(list[Tensor], device_max_exp_avg_sqs_)
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)  # type: ignore[assignment]

                # Set intermediate to the max. for normalizing running avg. of gradient when amsgrad
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_max_exp_avg_sqs)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_exp_avg_sqs)

            torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
            torch._foreach_add_(exp_avg_sq_sqrt, eps)
            torch._foreach_div_(exp_avg_sq_sqrt, step_size)

            # at this point, exp_avg_sq_sqrt = - (1 - beta^t) * [sqrt(exp_avg_sq / (1 - beta2^t)) + eps] / lr
            torch._foreach_addcdiv_(device_params, device_exp_avgs, exp_avg_sq_sqrt)
        else:
            bias_correction1 = [
                1 - beta1 ** _get_value(step) for step in device_state_steps
            ]
            bias_correction2 = [
                1 - beta2 ** _get_value(step) for step in device_state_steps
            ]

            step_size = _stack_if_compiling([(lr / bc) * -1 for bc in bias_correction1])

            bias_correction2_sqrt = [bc**0.5 for bc in bias_correction2]  # type: ignore[arg-type]

            if amsgrad:
                device_max_exp_avg_sqs = cast(list[Tensor], device_max_exp_avg_sqs_)
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)

                # Use the max. for normalizing running avg. of gradient
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_max_exp_avg_sqs)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_exp_avg_sqs)

            torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
            torch._foreach_add_(exp_avg_sq_sqrt, eps)
            torch._foreach_addcdiv_(
                device_params,
                device_exp_avgs,
                exp_avg_sq_sqrt,
                step_size,  # type: ignore[arg-type]
            )


def _fused_adam(
    params: list[Tensor],
    grads: list[Tensor],
    exp_avgs: list[Tensor],
    exp_avg_sqs: list[Tensor],
    max_exp_avg_sqs: list[Tensor],
    state_steps: list[Tensor],
    grad_scale: Tensor | None,
    found_inf: Tensor | None,
    *,
    amsgrad: bool,
    has_complex: bool,  # Needed for consistency.
    beta1: float | Tensor,
    beta2: float | Tensor,
    lr: float | Tensor,
    weight_decay: float,
    eps: float,
    maximize: bool,
    capturable: bool,  # Needed for consistency.
    differentiable: bool,
    decoupled_weight_decay: bool,
) -> None:
    if not params:
        return
    if differentiable:
        raise RuntimeError("Adam with fused=True does not support differentiable=True")

    beta1 = _to_scalar(beta1)
    beta2 = _to_scalar(beta2)

    grad_scale_dict: DeviceDict = (
        {grad_scale.device: grad_scale} if grad_scale is not None else {}
    )
    found_inf_dict: DeviceDict = (
        {found_inf.device: found_inf} if found_inf is not None else {}
    )

    # We only shuffle around the lr when it is a Tensor and on CUDA, otherwise, we prefer
    # treating it as a scalar.
    lr_dict: DeviceDict | None = (
        {lr.device: lr} if isinstance(lr, Tensor) and str(lr.device) != "cpu" else None
    )
    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
        [params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps]  # type: ignore[list-item]
    )
    for (device, _), (
        (
            device_params_,
            device_grads_,
            device_exp_avgs_,
            device_exp_avg_sqs_,
            device_max_exp_avg_sqs,
            device_state_steps_,
        ),
        _,
    ) in grouped_tensors.items():
        device_params = cast(list[Tensor], device_params_)
        device_grads = cast(list[Tensor], device_grads_)
        device_exp_avgs = cast(list[Tensor], device_exp_avgs_)
        device_exp_avg_sqs = cast(list[Tensor], device_exp_avg_sqs_)
        device_state_steps = cast(list[Tensor], device_state_steps_)

        device_grad_scale, device_found_inf = None, None
        if grad_scale is not None:
            device_grad_scale = grad_scale_dict.setdefault(
                device, grad_scale.to(device, non_blocking=True)
            )
        if found_inf is not None:
            device_found_inf = found_inf_dict.setdefault(
                device, found_inf.to(device, non_blocking=True)
            )
        if lr_dict is not None and device not in lr_dict:
            lr_dict[device] = lr.to(device=device, non_blocking=True)  # type: ignore[union-attr]
            lr = lr_dict[device]
        torch._foreach_add_(device_state_steps, 1)
        func = torch._fused_adam_ if not decoupled_weight_decay else torch._fused_adamw_
        # pyrefly: ignore [no-matching-overload]
        func(
            device_params,
            device_grads,
            device_exp_avgs,
            device_exp_avg_sqs,
            device_max_exp_avg_sqs,  # type: ignore[arg-type]
            device_state_steps,
            amsgrad=amsgrad,
            lr=lr,  # type: ignore[arg-type]
            beta1=beta1,
            beta2=beta2,
            weight_decay=weight_decay,
            eps=eps,
            maximize=maximize,
            grad_scale=device_grad_scale,
            found_inf=device_found_inf,
        )
        if device_found_inf is not None:
            torch._foreach_sub_(
                device_state_steps, [device_found_inf] * len(device_state_steps)
            )


@_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_adam)
def adam(
    params: list[Tensor],
    grads: list[Tensor],
    exp_avgs: list[Tensor],
    exp_avg_sqs: list[Tensor],
    max_exp_avg_sqs: 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
    foreach: bool | None = None,
    capturable: bool = False,
    differentiable: bool = False,
    fused: bool | None = None,
    grad_scale: Tensor | None = None,
    found_inf: Tensor | None = None,
    has_complex: bool = False,
    decoupled_weight_decay: bool = False,
    *,
    amsgrad: bool,
    beta1: float | Tensor,
    beta2: float | Tensor,
    lr: float | Tensor,
    weight_decay: float,
    eps: float,
    maximize: bool,
) -> None:
    r"""Functional API that performs Adam algorithm computation.

    See :class:`~torch.optim.Adam` for details.
    """
    # Respect when the user inputs False/True for foreach or fused. We only want to change
    # the default when neither have been user-specified. Note that we default to foreach
    # and pass False to use_fused. This is not a mistake--we want to give the fused impl
    # bake-in time before making it the default, even if it is typically faster.
    if fused is None and foreach is None:
        _, foreach = _default_to_fused_or_foreach(
            params, differentiable, use_fused=False
        )
        # Do not flip on foreach for the unsupported case where lr is a Tensor and capturable=False.
        if foreach and isinstance(lr, Tensor) and not capturable:
            foreach = False
    if fused is None:
        fused = False
    if foreach is None:
        foreach = False

    # this check is slow during compilation, so we skip it
    # if it's strictly needed we can add this check back in dynamo
    if not torch.compiler.is_compiling() and 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 foreach and torch.jit.is_scripting():
        raise RuntimeError("torch.jit.script not supported with foreach optimizers")
    if fused and torch.jit.is_scripting():
        raise RuntimeError("torch.jit.script not supported with fused optimizers")

    if fused and not torch.jit.is_scripting():
        func = _fused_adam
    elif foreach and not torch.jit.is_scripting():
        func = _multi_tensor_adam
    else:
        func = _single_tensor_adam

    func(
        params,
        grads,
        exp_avgs,
        exp_avg_sqs,
        max_exp_avg_sqs,
        state_steps,
        amsgrad=amsgrad,
        has_complex=has_complex,
        beta1=beta1,
        beta2=beta2,
        lr=lr,
        weight_decay=weight_decay,
        eps=eps,
        maximize=maximize,
        capturable=capturable,
        differentiable=differentiable,
        grad_scale=grad_scale,
        found_inf=found_inf,
        decoupled_weight_decay=decoupled_weight_decay,
    )