# Source code for torch.optim.adam

    from collections import defaultdict
    import math
    from typing import cast, List, Optional, Dict, Tuple

    import torch
    from torch import Tensor
    from .optimizer import Optimizer, _use_grad_for_differentiable

    __all__ = ['Adam', 'adam']

    # TODO(crcrpar): Move this to soemwhere (e.g. torch/optim/_utils?) else when adding another fused optimizer.
    # NOTE(crcrpar): Almost the same as `_MultiDeviceReplicator` defined in
    # torch/cuda/amp/grad_scaler.py except for the key being str only for torch script.
    class _MultiDeviceReplicator:
        main_tensor: Tensor
        _per_device_tensors: Dict[str, Tensor]

        def __init__(self, main_tensor: Tensor) -> None:
            self.main_tensor = main_tensor
            self._per_device_tensors = {str(main_tensor.device): main_tensor}

        def get(self, device: str):
            if device in self._per_device_tensors:
                return self._per_device_tensors[device]
            tensor = self.main_tensor.to(device=device, non_blocking=True, copy=True)
            self._per_device_tensors[device] = tensor
            return tensor

    # todo(crcrpar): Move this to another place when adding another fused optimizer.
    def _get_fp16AMP_params(
        *,
        optimizer: Optimizer,
        grad_scaler: Optional[torch.cuda.amp.GradScaler] = None,
        device: torch.device,
    ) -> Optional[_MultiDeviceReplicator]:
        if grad_scaler is None:
            return None
        found_inf_dict = grad_scaler._check_inf_per_device(optimizer)
        # Combines found_inf tensors from all devices. As in GradScaler.update(),
        # tensors are combined on the scale's device, which is an arbitrary but
        # reasonable choice that avoids new context creation.
        found_infs = [f.to(device, non_blocking=True) for f in found_inf_dict.values()]
        assert len(found_infs) > 0, "No inf checks were recorded in _check_inf_per_device."
        with torch.no_grad():
            found_inf_combined = cast(torch.Tensor, sum(found_infs))
        return _MultiDeviceReplicator(found_inf_combined)

    class Adam(Optimizer):
        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}                                                              \\
                &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                    v_0\leftarrow 0 \text{ (second moment)},\: \widehat{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}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                   \\
                &\hspace{5mm}\textbf{if} \: amsgrad                                                  \\
                &\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max},
                    \widehat{v_t})                                                                   \\
                &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
                    \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big)                                 \\
                &\hspace{5mm}\textbf{else}                                                           \\
                &\hspace{10mm}\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`_.

        Args:
            params (iterable): iterable of parameters to optimize or dicts defining
                parameter groups
            lr (float, optional): learning rate (default: 1e-3)
            betas (Tuple[float, float], optional): coefficients used for computing
                running averages of gradient and its square (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)
            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 (bool, optional): whether foreach implementation of optimizer
                is used (default: None)
            maximize (bool, optional): maximize the params based on the objective, instead of
                minimizing (default: False)
            capturable (bool, optional): whether this instance is safe to capture in a CUDA graph.
                Passing True can impair ungraphed performance, so if you don't intend to
                graph capture this instance, leave it False (default: False)
            fused (bool, optional): whether fused implementation of optimizer is used.
                Currently, `torch.float64`, `torch.float32`, `torch.float16`, and `torch.bfloat16`
                are supported. (default: False)

        .. _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 __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                     weight_decay=0, amsgrad=False, *, foreach: Optional[bool] = None,
                     maximize: bool = False, capturable: bool = False,
                     differentiable: bool = False, fused: bool = False):
            if not 0.0 <= lr:
                raise ValueError("Invalid learning rate: {}".format(lr))
            if not 0.0 <= eps:
                raise ValueError("Invalid epsilon value: {}".format(eps))
            if not 0.0 <= betas[0] < 1.0:
                raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
            if not 0.0 <= betas[1] < 1.0:
                raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
            if not 0.0 <= weight_decay:
                raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
            defaults = dict(lr=lr, betas=betas, eps=eps,
                            weight_decay=weight_decay, amsgrad=amsgrad,
                            maximize=maximize, foreach=foreach, capturable=capturable,
                            differentiable=differentiable, fused=fused)
            super(Adam, self).__init__(params, defaults)

            if fused:
                if differentiable:
                    raise RuntimeError("`fused` cannot be `differentiable`")
                self._step_supports_amp_scaling = True
                # TODO(crcrpar): [low prec params & their higher prec copy]
                # Suppor 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 not all(
                    p.is_cuda and torch.is_floating_point(p)
                    for pg in self.param_groups for p in pg['params']
                ):
                    raise RuntimeError("FusedAdam requires all the params to be CUDA, floating point")

        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('fused', False)
            state_values = list(self.state.values())
            step_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['step'])
            if not step_is_tensor:
                for s in state_values:
                    s['step'] = torch.tensor(float(s['step']))

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

            Args:
                closure (Callable, optional): A closure that reevaluates the model
                    and returns the loss.
                grad_scaler (:class:`torch.cuda.amp.GradScaler`, optional): A GradScaler which is
                    supplied from ``grad_scaler.step(optimizer)``.
            """
            self._cuda_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 = []
                grads = []
                exp_avgs = []
                exp_avg_sqs = []
                max_exp_avg_sqs = []
                state_steps = []
                beta1, beta2 = group['betas']

                grad_scale = None
                found_inf = None
                if group['fused'] and grad_scaler is not None:
                    grad_scale = grad_scaler._get_scale_async()
                    device = grad_scale.device
                    grad_scale = _MultiDeviceReplicator(grad_scale)
                    found_inf = _get_fp16AMP_params(optimizer=self, grad_scaler=grad_scaler, device=device)

                for p in group['params']:
                    if p.grad is not None:
                        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:
                            state['step'] = (
                                torch.zeros((1,), dtype=torch.float, device=p.device)
                                if self.defaults['capturable'] or self.defaults['fused']
                                else torch.tensor(0.)
                            )
                            # 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')
                        state_steps.append(state['step'])

                adam(params_with_grad,
                     grads,
                     exp_avgs,
                     exp_avg_sqs,
                     max_exp_avg_sqs,
                     state_steps,
                     amsgrad=group['amsgrad'],
                     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=grad_scale,
                     found_inf=found_inf)

            return loss

    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: Optional[bool] = None,
             capturable: bool = False,
             differentiable: bool = False,
             fused: bool = False,
             grad_scale: Optional[_MultiDeviceReplicator] = None,
             found_inf: Optional[_MultiDeviceReplicator] = None,
             *,
             amsgrad: bool,
             beta1: float,
             beta2: float,
             lr: float,
             weight_decay: float,
             eps: float,
             maximize: bool):
        r"""Functional API that performs Adam algorithm computation.
        See :class:`~torch.optim.Adam` 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 foreach is None:
            # Placeholder for more complex foreach logic to be added when value is not set
            foreach = 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_adam
        elif fused and not torch.jit.is_scripting():
            func = _fused_adam
        else:
            func = _single_tensor_adam

        func(params,
             grads,
             exp_avgs,
             exp_avg_sqs,
             max_exp_avg_sqs,
             state_steps,
             amsgrad=amsgrad,
             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)

    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: Optional[_MultiDeviceReplicator],
                            found_inf: Optional[_MultiDeviceReplicator],
                            *,
                            amsgrad: bool,
                            beta1: float,
                            beta2: float,
                            lr: float,
                            weight_decay: float,
                            eps: float,
                            maximize: bool,
                            capturable: bool,
                            differentiable: bool):

        assert grad_scale is None and found_inf is 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 capturable:
                assert param.is_cuda and step_t.is_cuda, "If capturable=True, params and state_steps must be CUDA tensors."

            # update step
            step_t += 1

            if weight_decay != 0:
                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)
                param = torch.view_as_real(param)

            # Decay the first and second moment running average coefficient
            exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
            exp_avg_sq.mul_(beta2).addcmul_(grad, grad.conj(), value=1 - beta2)

            if capturable or differentiable:
                step = step_t

                # 1 - beta1 ** step can't be captured in a CUDA graph, even if step is a CUDA tensor
                # (incurs "RuntimeError: CUDA error: operation not permitted when stream is capturing")
                bias_correction1 = 1 - torch.pow(beta1, step)
                bias_correction2 = 1 - torch.pow(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_sqs_i = max_exp_avg_sqs[i].clone()
                    else:
                        max_exp_avg_sqs_i = max_exp_avg_sqs[i]
                    max_exp_avg_sqs[i].copy_(torch.maximum(max_exp_avg_sqs_i, 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)

                param.addcdiv_(exp_avg, denom)
            else:
                step = step_t.item()

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

                step_size = lr / bias_correction1

                bias_correction2_sqrt = math.sqrt(bias_correction2)

                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)

    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: Optional[_MultiDeviceReplicator],
                           found_inf: Optional[_MultiDeviceReplicator],
                           *,
                           amsgrad: bool,
                           beta1: float,
                           beta2: float,
                           lr: float,
                           weight_decay: float,
                           eps: float,
                           maximize: bool,
                           capturable: bool,
                           differentiable: bool):
        if len(params) == 0:
            return

        if capturable:
            assert all(p.is_cuda and step.is_cuda for p, step in zip(params, state_steps)), \
                "If capturable=True, params and state_steps must be CUDA tensors."

        assert grad_scale is None and found_inf is None

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

        assert not differentiable, "_foreach ops don't support autograd"
        # Handle complex parameters
        grads = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grads]
        exp_avgs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avgs]
        exp_avg_sqs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avg_sqs]
        params_ = [torch.view_as_real(x) if torch.is_complex(x) else x for x in params]

        # update steps
        torch._foreach_add_(state_steps, 1)

        if weight_decay != 0:
            torch._foreach_add_(grads, params, alpha=weight_decay)

        # Decay the first and second moment running average coefficient
        torch._foreach_mul_(exp_avgs, beta1)
        torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1)

        torch._foreach_mul_(exp_avg_sqs, beta2)
        torch._foreach_addcmul_(exp_avg_sqs, grads, grads, 1 - beta2)

        if capturable:
            # TODO: use foreach_pow if/when foreach_pow is added
            bias_correction1 = [torch.pow(beta1, step) for step in state_steps]
            bias_correction2 = [torch.pow(beta2, step) for step in state_steps]
            # foreach_sub doesn't allow a scalar as the first arg
            torch._foreach_sub_(bias_correction1, 1)
            torch._foreach_sub_(bias_correction2, 1)
            torch._foreach_neg_(bias_correction1)
            torch._foreach_neg_(bias_correction2)

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

            bias_correction2_sqrt = torch._foreach_sqrt(bias_correction2)

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(max_exp_avg_sqs, exp_avg_sqs)  # type: ignore[assignment]

                # Use the max. for normalizing running avg. of gradient
                max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs)
                # 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)
                torch._foreach_div_(max_exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size))
                eps_over_step_size = torch._foreach_div(step_size, eps)
                torch._foreach_reciprocal_(eps_over_step_size)
                denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps_over_step_size)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs)
                torch._foreach_div_(exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size))
                eps_over_step_size = torch._foreach_div(step_size, eps)
                torch._foreach_reciprocal_(eps_over_step_size)
                denom = torch._foreach_add(exp_avg_sq_sqrt, eps_over_step_size)

            torch._foreach_addcdiv_(params_, exp_avgs, denom)
        else:
            bias_correction1 = [1 - beta1 ** step.item() for step in state_steps]
            bias_correction2 = [1 - beta2 ** step.item() for step in state_steps]

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

            bias_correction2_sqrt = [math.sqrt(bc) for bc in bias_correction2]

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(max_exp_avg_sqs, exp_avg_sqs)

                # Use the max. for normalizing running avg. of gradient
                max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs)
                torch._foreach_div_(max_exp_avg_sq_sqrt, bias_correction2_sqrt)
                denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs)
                torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
                denom = torch._foreach_add(exp_avg_sq_sqrt, eps)

            torch._foreach_addcdiv_(params_, exp_avgs, denom, step_size)

    # TODO(crcrpar): Move this to another place when adding another fused optimizer.
    # TODO(crcrpar): Make this generic when there's more fused optimizers.
    # TODO(crcrpar): Think of rewriting this in C++.
    @torch.no_grad()
    def _group_params_by_device_and_dtype(
        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],
    ) -> Dict[Tuple[str, torch.dtype], List[List[Tensor]]]:
        per_device_and_dtype_tensors = defaultdict(lambda: [[] for _ in range(6)])
        for i, (p, step) in enumerate(zip(params, state_steps)):
            key = (str(p.device), p.dtype)
            per_device_and_dtype_tensors[key][0].append(p)
            per_device_and_dtype_tensors[key][1].append(grads[i])
            per_device_and_dtype_tensors[key][2].append(exp_avgs[i])
            per_device_and_dtype_tensors[key][3].append(exp_avg_sqs[i])
            if max_exp_avg_sqs:
                per_device_and_dtype_tensors[key][4].append(max_exp_avg_sqs[i])
            per_device_and_dtype_tensors[key][5].append(step)
        return per_device_and_dtype_tensors

    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: Optional[_MultiDeviceReplicator],
        found_inf: Optional[_MultiDeviceReplicator],
        *,
        amsgrad: bool,
        beta1: float,
        beta2: float,
        lr: float,
        weight_decay: float,
        eps: float,
        maximize: bool,
        capturable: bool,  # Needed for consistency.
        differentiable: bool,
    ) -> None:
        grouped_tensors = _group_params_by_device_and_dtype(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps)
        for (device, dtype) in grouped_tensors:
            (
                device_params,
                device_grads,
                device_exp_avgs,
                device_exp_avg_sqs,
                device_max_exp_avg_sqs,
                device_state_steps,
            ) = grouped_tensors[(device, dtype)]
            if grad_scale is not None and found_inf is not None:
                device_grad_scale = grad_scale.get(device)
                device_found_inf = found_inf.get(device)
            else:
                device_grad_scale = None
                device_found_inf = None
            torch._foreach_add_(device_state_steps, 1)
            torch._fused_adam_(
                device_params,
                device_grads,
                device_exp_avgs,
                device_exp_avg_sqs,
                device_max_exp_avg_sqs,
                device_state_steps,
                amsgrad=amsgrad,
                lr=lr,
                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))