  We investigate the training of sparse layers that use different parameters
for different inputs based on hashing in large Transformer models.
Specifically, we modify the feedforward layer to hash to different sets of
weights depending on the current token, over all tokens in the sequence. We
show that this procedure either outperforms or is competitive with
learning-to-route mixture-of-expert methods such as Switch Transformers and
BASE Layers, while requiring no routing parameters or extra terms in the
objective function such as a load balancing loss, and no sophisticated
assignment algorithm. We study the performance of different hashing techniques,
hash sizes and input features, and show that balanced and random hashes focused
on the most local features work best, compared to either learning clusters or
using longer-range context. We show our approach works well both on large
language modeling and dialogue tasks, and on downstream fine-tuning tasks.
