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.

Self-play has powered breakthroughs in two-player and multi-player games. Here we show that self-play is a surprisingly effective strategy in another domain. We show that robust and naturalistic driving emerges entirely from self-play in simulation at unprecedented scale -- 1.6 billion km of driving. This is enabled by Gigaflow, a batched simulator that can synthesize and train on 42 years of subjective driving experience per hour on a single 8-GPU node. The resulting policy achieves state-of-the-art performance on three independent autonomous driving benchmarks. The policy outperforms the prior state of the art when tested on recorded real-world scenarios, amidst human drivers, without ever seeing human data during training. The policy is realistic when assessed against human references and achieves unprecedented robustness, averaging 17.5 years of continuous driving between incidents in simulation.