# Nested Byte-Level Vocabularies Are Cheap to Deploy and Expensive to Share: A Pre-Registered Negative Result

arXiv: https://arxiv.org/abs/2608.28151 · HTML: https://mlsanity.com/paper/2608.28151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 7 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Subword Regularization: Improving Neural Network Translation Models with Multiple Subword Candidates](https://mlsanity.com/paper/1804.10959/) (2018)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [BPE-Dropout: Simple and Effective Subword Regularization](https://mlsanity.com/paper/1910.13267/) (2019)
- [MatFormer: Nested Transformer for Elastic Inference](https://mlsanity.com/paper/2310.07707/) (2023)

## Abstract (arXiv)

A byte-level BPE tokenizer is an ordered list of merge rules, so applying only a prefix yields a vocabulary whose token identifiers are the first rows of the full vocabulary. This prefix nesting allows one language model to operate at several vocabulary sizes, use a control token to indicate the active size, and be deployed at any trained size by slicing its embedding and output head. We pre-registered five claims, including margins, seeds, contrasts, and a stop rule, and trained 30 models with 3.1M- and 10.6M-parameter bodies on 200M tokens each. Slicing is numerically exact: across 76 checks, a sliced model reproduces the restricted full model's logits bit for bit and removes 66% of deployed weights without changing latency. However, the shared model trails a fixed-cap specialist by 3.64% bits per byte at 32k against a 1% margin, and by 2.96% at 8k against a 2% margin. A 2x2 ablation separating the control token from output restriction finds that the token changes performance by +0.07% to +0.13%, with all intervals crossing zero, while output restriction costs +0.47% to +1.19%; the factors are substitutes rather than complements. Multi-cap training nevertheless improves robustness: under typographical noise, the same checkpoint degrades 12.5--15.4 points less in its fine mode and outperforms each fixed-cap specialist at that specialist's vocabulary size. A control with neither cap token nor output restriction is equally robust, attributing this benefit to multi-granularity training rather than conditioning. The per-cap penalty tracks each cap's share of training rows, yielding a falsifiable prediction for future work.