text: from typing import Sequence, Union
  
  import torch
  
  from ignite.exceptions import NotComputableError
  from ignite.metrics.metric import Metric, reinit__is_reduced, sync_all_reduce
  
  __all__ = ["MeanSquaredError"]
  
  
  class MeanSquaredError(Metric):
      r"""Calculates the `mean squared error <https://en.wikipedia.org/wiki/Mean_squared_error>`_.
  
      .. math:: \text{MSE} = \frac{1}{N} \sum_{i=1}^N \left(y_{i} - x_{i} \right)^2
  
      where :math:`y_{i}` is the prediction tensor and :math:`x_{i}` is ground true tensor.
  
      - ``update`` must receive output of the form ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
  
      Args:
          output_transform: a callable that is used to transform the
              :class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
              form expected by the metric. This can be useful if, for example, you have a multi-output model and
              you want to compute the metric with respect to one of the outputs.
              By default, metrics require the output as ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
          device: specifies which device updates are accumulated on. Setting the
              metric's device to be the same as your ``update`` arguments ensures the ``update`` method is
              non-blocking. By default, CPU.
  
      Examples:
          To use with ``Engine`` and ``process_function``, simply attach the metric instance to the engine.
          The output of the engine's ``process_function`` needs to be in the format of
          ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y, ...}``. If not, ``output_tranform`` can be added
          to the metric to transform the output into the form expected by the metric.
  
          ``y_pred`` and ``y`` should have the same shape.
  
          .. include:: defaults.rst
              :start-after: :orphan:
  
          .. testcode::
  
              metric = MeanSquaredError()
              metric.attach(default_evaluator, 'mse')
              preds = torch.Tensor([
                  [1, 2, 4, 1],
                  [2, 3, 1, 5],
                  [1, 3, 5, 1],
                  [1, 5, 1 ,11]
              ])
              target = preds * 0.75
              state = default_evaluator.run([[preds, target]])
              print(state.metrics['mse'])
  
          .. testoutput::
  
              3.828125
      """
  
      @reinit__is_reduced
      def reset(self) -> None:
          self._sum_of_squared_errors = torch.tensor(0.0, device=self._device)
          self._num_examples = 0
  
      @reinit__is_reduced
      def update(self, output: Sequence[torch.Tensor]) -> None:
          y_pred, y = output[0].detach(), output[1].detach()
          squared_errors = torch.pow(y_pred - y.view_as(y_pred), 2)
          self._sum_of_squared_errors += torch.sum(squared_errors).to(self._device)
          self._num_examples += y.shape[0]
  
      @sync_all_reduce("_sum_of_squared_errors", "_num_examples")
      def compute(self) -> Union[float, torch.Tensor]:
          if self._num_examples == 0:
              raise NotComputableError("MeanSquaredError must have at least one example before it can be computed.")
          return self._sum_of_squared_errors.item() / self._num_examples
  