Cut Your Losses in Large-Vocabulary Language Models
Authors: name: Erik Wijmans, name: Brody Huval, name: Alexander Hertzberg, name: Vladlen Koltun, name: Philipp Krähenbühl

As language models grow ever larger, so do their vocabularies. This has
shifted the memory footprint of LLMs during training disproportionately to one
single layer: the cross-entropy in the loss computation. Cross-entropy builds
up a logit matrix with entries for each pair of input tokens and vocabulary
items and, for small models, consumes an order of magnitude more memory than
the rest of the LLM combined. We propose Cut Cross-Entropy (CCE), a method that
computes the cross-entropy loss without materializing the logits for all tokens
into global memory. Rather, CCE only computes the logit for the correct token
and evaluates the log-sum-exp over all logits on the fly. We implement a custom
kernel that performs the matrix multiplications and the log-sum-exp reduction
over the vocabulary in flash memory, making global memory consumption for the
cross-entropy computation negligible. This has a dramatic effect. Taking the
Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss
computation from 24 GB to 1 MB, and the total training-time memory consumption
of the classifier head from 28 GB to 1 GB. To improve the throughput of CCE, we
leverage the inherent sparsity of softmax and propose to skip elements of the
gradient computation that have a negligible (i.e., below numerical precision)
contribution to the gradient. Experiments demonstrate that the dramatic
reduction in memory consumption is accomplished without sacrificing training
speed or convergence.