def mass_preservation(
    alpha: Tensor,
    padding_mask: Optional[Tensor] = None,
    left_padding: bool = False
):
    """
    Function to compute the mass perservation for alpha.
    This means that the residual weights of alpha will be assigned
    to the last token.

    Reference:
    Monotonic Infinite Lookback Attention for Simultaneous Machine Translation
    https://arxiv.org/abs/1906.05218

    alpha: bsz, tgt_len, src_len
    padding_mask: bsz, src_len
    left_padding: bool
    """

    prob_check(alpha)

    if padding_mask is not None:
        if not left_padding:
            assert not padding_mask[:, 0].any(), (
                "Find padding on the beginning of the sequence."
            )
        alpha = alpha.masked_fill(padding_mask.unsqueeze(1), 0.0)

    if left_padding or padding_mask is None:
        residuals = 1 - alpha[:, :, :-1].sum(dim=-1).clamp(0, 1)
        alpha[:, :, -1] = residuals
    else:
        # right padding
        _, tgt_len, src_len = alpha.size()
        residuals = 1 - alpha.sum(dim=-1, keepdim=True).clamp(0, 1)
        src_lens = src_len - padding_mask.sum(dim=1, keepdim=True)
        src_lens = src_lens.expand(-1, tgt_len).contiguous()
        # add back the last value
        residuals += alpha.gather(2, src_lens.unsqueeze(2) - 1)
        alpha = alpha.scatter(2, src_lens.unsqueeze(2) - 1, residuals)

        prob_check(alpha)

    return alpha

    Function to compute the mass perservation for alpha.
    This means that the residual weights of alpha will be assigned
    to the last token.

    Reference:
    Monotonic Infinite Lookback Attention for Simultaneous Machine Translation
    https://arxiv.org/abs/1906.05218

    alpha: bsz, tgt_len, src_len
    padding_mask: bsz, src_len
    left_padding: bool
    
understand_icl/fairseq/examples/simultaneous_translation/utils/monotonic_attention.py