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arXiv · 2605.22821

Tokenisation via Convex Relaxations

Jan Tempus·Philip Whittington·Craig W. Schmidt·Dennis Komm·Tiago Pimentel
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Abstract

Tokenisation is an integral part of the current NLP pipeline. Current tokenisation algorithms such as BPE and Unigram are greedy algorithms -- they make locally optimal decisions without considering the resulting vocabulary as a whole. We instead formulate tokeniser construction as a linear program and solve it using convex optimisation tools, yielding a new algorithm we call ConvexTok. We find ConvexTok consistently improves intrinsic tokenisation metrics and the bits-per-byte (BpB) achieved by language models; it also improves downstream task performance, but less consistently. Furthermore, ConvexTok allows the user to certify how far their tokeniser is from optimal, with respect to a certain objective, via a lower bound, and we empirically find it to be within 1\% of optimal at common vocabulary sizes.

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Jan Tempus, Philip Whittington, Craig W. Schmidt, Dennis Komm, Tiago Pimentel. 2026-05-21. Tokenisation via Convex Relaxations. https://arxiv.org/abs/2605.22821

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