If you just want to see the code, it’s in a gist.

## Introduction: Sequence tokenization and padding

Sometimes the fact that all proteins are not the same length is the bane of my existence.

One way we deal with variable-length sequences in machine learning is to pad them all to the same length. For example, if I have the following nucleotide sequences:

AGCTAG
AGCTAGA
AGCTA


I can right-pad them by introducing a special padding token, let’s call it p.

AGCTAGp
AGCTAGA
AGCTApp


And then I can use this as a batch input to the machine-learning model of my choice by assigning each nucleotide and the padding token an integer:

x = torch.tensor(
[
[0, 2, 1, 3, 0, 2, 4],
[0, 2, 1, 3, 0, 2, 0],
[0, 2, 1, 3, 0, 4, 4]
]
)


If I want to put sequences through a transformer or RNN or CNN and I don’t want the model to be affected by the padding, I can also pass in a mask (mask = (x != 4)) and use that mask to set things to zero where appropriate. For example, the PyTorch Transformer class uses this sort of mask (but with a ByteTensor) for its [src/tgt/mask]_padding_mask arguments.

## Trying to extend PyTorch’s batchnorm

Unfortunately, nn.BatchNorm1d doesn’t support this type of masking, so if I zero out padding locations, then my minibatch statistics get artificially lowered by the extra zeros. Given Pytorch’s object-oriented nature, the most elegant way to implement masked batchnorm would be to extend one of their classes and modify the way minibatch statistics are calculated.

Starting at nn.BatchNorm1d, we find that all this class implements is a method for checking input dimensions:

    def _check_input_dim(self, input):
if input.dim() != 2 and input.dim() != 3:
raise ValueError('expected 2D or 3D input (got {}D input)'
.format(input.dim()))


It’s superclass (nn._BatchNorm) has a forward method, which checks whether to use train or eval mode, retrieves the parameters needed to calculate the moving averages, and then calls F.batch_norm. F.batch_norm in turn calls torch.batch_norm. Clicking on that in github leads back to F.batch_norm: I think it must be actually implemented in the lower-level cpp code.

In any case, it looks like there’s no straight-forward way to extend PyTorch’s batchnorm implementation, so time to write it from scratch.

Given a (B, 1, L) mask, we first mask and then compute the number of unmasked locations over which to calculate the minibatch statistics:

if input_mask is not None:


Then calculate the minibatch mean:

masked_sum = masked.sum(dim=0, keepdim=True).sum(dim=2, keepdim=True)



And the minibatch variance:

current_var = ((masked - current_mean) ** 2)
current_var = current_var.sum(dim=0, keepdim=True).sum(dim=2, keepdim=True) / n



The full module is available as a gist.

## Limitations

Because I didn’t want to dig deeper into PyTorch source, there’s a few limitations here.

1. It’s almost certainly not as fast as the native PyTorch implementation.
2. If you’re doing multi-GPU training, minibatch statistics won’t be synced across devices as they would be with Apex’s SyncBatchNorm.
3. If you’re doing mixed-precision training with Apex, you can’t use level O2 because it won’t detect that this is a batchnorm layer and keep it in float precision.