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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def forward(self, tensors: List[torch.Tensor], # pylint: disable=arguments-differ mask: torch.Tensor = None) -> torch.Tensor: """ Compute a weighted average of the ``tensors``. The input tensors an be any shape with at least two dimensions, but must all be the same shape. When ``do_layer_norm=True``, the ``mask`` is required input. If the ``tensors`` are ``(batch_size, timesteps, dim)`` and ``mask`` of shape ``(batch_size, timesteps)``. When ``do_layer_norm=False`` the ``mask`` is ignored. """

        if len(tensors) != self.mixture_size:
            raise ConfigurationError("{} tensors were passed, but the module was initialized to "
                                     "mix {} tensors.".format(len(tensors), self.mixture_size))

        def _do_layer_norm(tensor, broadcast_mask, num_elements_not_masked):
            tensor_masked = tensor * broadcast_mask
            mean = torch.sum(tensor_masked) / num_elements_not_masked
            variance = torch.sum(((tensor_masked - mean) * broadcast_mask)**2) / num_elements_not_masked
            return (tensor - mean) / torch.sqrt(variance + 1E-12)

        normed_weights = torch.nn.functional.softmax(torch.cat([parameter for parameter
                                                                in self.scalar_parameters]), dim=0)
        normed_weights = torch.split(normed_weights, split_size_or_sections=1)

        if not self.do_layer_norm:
            pieces = []
            for weight, tensor in zip(normed_weights, tensors):
                pieces.append(weight * tensor)
            return self.gamma * sum(pieces)

        else:
            mask_float = mask.float()
            broadcast_mask = mask_float.unsqueeze(-1)
            input_dim = tensors[0].size(-1)
            num_elements_not_masked = torch.sum(mask_float) * input_dim

            pieces = []
            for weight, tensor in zip(normed_weights, tensors):
                pieces.append(weight * _do_layer_norm(tensor,
                                                      broadcast_mask, num_elements_not_masked))
            return self.gamma * sum(pieces)