Exact Byte-Level Probabilities from Tokenized Language Models for FIM-Tasks and Model Ensembles

TL;DR

This paper introduces a method to derive exact byte-level probabilities from tokenized language models, addressing tokenization bias and enabling improved performance in fill-in-the-middle tasks and model ensembles without additional training.

Contribution

It presents the Byte-Token Representation Lemma and a zero-shot algorithm to convert tokenized models into byte-level models, mitigating tokenization bias in a novel way.

Findings

18% improvement in FIM benchmarks

Seamless integration of models with different vocabularies

Up to 3.7% performance gain in model ensembles

Abstract

Tokenization is associated with many poorly understood shortcomings in language models (LMs), yet remains an important component for long sequence scaling purposes. This work studies how tokenization impacts model performance by analyzing and comparing the stochastic behavior of tokenized models with their byte-level, or token-free, counterparts. We discover that, even when the two models are statistically equivalent, their predictive distributions over the next byte can be substantially different, a phenomenon we term as ``tokenization bias''. To fully characterize this phenomenon, we introduce the Byte-Token Representation Lemma, a framework that establishes a mapping between the learned token distribution and its equivalent byte-level distribution. From this result, we develop a next-byte sampling algorithm that eliminates tokenization bias without requiring further training or optimization. In other words, this enables zero-shot conversion of tokenized LMs into statistically equivalent token-free ones. We demonstrate its broad applicability with two use cases: fill-in-the-middle (FIM) tasks and model ensembles. In FIM tasks where input prompts may terminate mid-token, leading to out-of-distribution tokenization, our method mitigates performance degradation and achieves 18% improvement in FIM coding benchmarks, while consistently outperforming the standard token healing fix. For model ensembles where each model employs a distinct vocabulary, our approach enables seamless integration, resulting in improved performance up to 3.7% over individual models across various standard baselines in reasoning, knowledge, and coding. Code is available at: https://github.com/facebookresearch/Exact-Byte-Level-Probabilities-from-Tokenized-LMs