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

        Args:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:
            for p in group["params"]:
                if p.grad is None:
                    continue
                grad = p.grad.data
                if grad.dtype in {torch.float16, torch.bfloat16}:
                    grad = grad.float()
                if grad.is_sparse:
                    raise RuntimeError(
                        "Adam does not support sparse gradients, please consider SparseAdam instead"
                    )
                amsgrad = group.get("amsgrad", False)

                p_data_fp32 = p.data
                if p.data.dtype in {torch.float16, torch.bfloat16}:
                    p_data_fp32 = p_data_fp32.float()

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state["step"] = 0
                    # Exponential moving average of gradient values
                    state["exp_avg"] = torch.zeros_like(p_data_fp32)
                    # Exponential moving average of squared gradient values
                    state["exp_avg_sq"] = torch.zeros_like(p_data_fp32)
                    if amsgrad:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state["max_exp_avg_sq"] = torch.zeros_like(p_data_fp32)
                else:
                    state["exp_avg"] = state["exp_avg"].to(p_data_fp32)
                    state["exp_avg_sq"] = state["exp_avg_sq"].to(p_data_fp32)
                    if amsgrad:
                        state["max_exp_avg_sq"] = state["max_exp_avg_sq"].to(
                            p_data_fp32
                        )

                exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
                if amsgrad:
                    max_exp_avg_sq = state["max_exp_avg_sq"]
                beta1, beta2 = group["betas"]

                state["step"] += 1

                # 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, value=1 - beta2)
                if amsgrad:
                    # Maintains the maximum of all 2nd moment running avg. till now
                    torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                    # Use the max. for normalizing running avg. of gradient
                    denom = max_exp_avg_sq.sqrt().add_(group["eps"])
                else:
                    denom = exp_avg_sq.sqrt().add_(group["eps"])

                bias_correction1 = 1 - beta1 ** state["step"]
                bias_correction2 = 1 - beta2 ** state["step"]
                step_size = group["lr"] * math.sqrt(bias_correction2) / bias_correction1

                if group["weight_decay"] != 0:
                    p_data_fp32.add_(
                        p_data_fp32, alpha=-group["weight_decay"] * group["lr"]
                    )

                p_data_fp32.addcdiv_(exp_avg, denom, value=-step_size)

                if p.data.dtype in {torch.float16, torch.bfloat16}:
                    p.data.copy_(p_data_fp32)

        return loss
Performs a single optimization step.

Args:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
fairseq/optim/adam.py