SOMBRERO: Measuring and Steering Boundary Placement in End-to-End Hierarchical Sequence Models

Hierarchical sequence models replace fixed tokenization with learned segmentations that compress long byte sequences for efficient autoregressive modeling. While recent end-to-end methods can learn meaningful boundaries from the language-modeling objective alone, it remains difficult to quantitatively assess and systematically steer where compute is spent. We introduce a router-agnostic metric of boundary quality, boundary enrichment B, which measures how strongly chunk starts concentrate on positions with high next-byte surprisal. Guided by this metric, we propose Sombrero, which steers boundary placement toward predictive difficulty via a confidence-alignment boundary loss and stabilizes boundary learning by applying confidence-weighted smoothing at the input level rather than on realized chunks. On 1B scale, across UTF-8 corpora covering English and German text as well as code and mathematical content, Sombrero improves the accuracy-efficiency trade-off and yields boundaries that more consistently align compute with hard-to-predict positions.