keras/src/backend/torch/optimizers/torch_adamax.py/Adamax/_parallel_update_step
class Adamax:    def _parallel_update_step(
        self,
        grads,
        variables,
        learning_rate,
    ):
        keras_variables = variables
        variables = [v.value for v in variables]

        dtype = variables[0].dtype
        lr = ops.cast(learning_rate, dtype)

        local_step = ops.cast(self.iterations + 1, dtype)

        beta_1_power = ops.power(ops.cast(self.beta_1, dtype), local_step)

        m_list = [
            self._m[self._get_variable_index(variable)].value
            for variable in keras_variables
        ]
        u_list = [
            self._u[self._get_variable_index(variable)].value
            for variable in keras_variables
        ]

        torch._foreach_mul_(m_list, self.beta_1)
        torch._foreach_add_(m_list, grads, alpha=1 - self.beta_1)

        torch._foreach_mul_(u_list, self.beta_2)
        torch._foreach_maximum_(u_list, torch._foreach_abs(grads))

        torch._foreach_add_(
            variables,
            torch._foreach_div(
                torch._foreach_mul(m_list, lr),
                torch._foreach_mul(
                    torch._foreach_add(u_list, self.epsilon),
                    1 - beta_1_power,
                ),
            ),
            alpha=-1,
        )