Easy to anticipate, hard to compute: boundary dependence finds the computed outputs that entropy patching misses

Nicolás Vera Zúñiga

Byte-level language models such as the Byte Latent Transformer (BLT) group bytes into patches and run their large global model once per patch. BLT starts a patch where a small model's next-byte entropy is high, so global compute goes where the next byte is hard to predict. We show that this rule has a systematic blind spot: positions whose type is predictable but whose value must be computed, such as the number after "=" in a worked math solution. Under tight patch budgets, entropy-triggered layouts skip these positions, and accuracy on them collapses. In Meta's BLT-1B with patch starts on 10% of bytes, the entropy rule puts a patch start at 16% of the computed results in GSM8K solutions and gets 19.0% of them exactly right; a boundary after each "=" at the same patch count gets 51.8%, and entropy combined with a label-free boundary-dependence signal gets 67.1% (default layout at 26% of bytes: 76.8%). The gap survives adapting BLT-1B to the budget with low-rank fine-tuning (32.9% vs 72.7%, three runs per rule, paired p < 1e-200) and grows with model size in byte models trained from scratch at a 10% budget: at 1M, 12M and 50M parameters, boundary dependence beats entropy on final…