Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A partition cover approach to tokenization (2501.06246v2)

Published 8 Jan 2025 in cs.CL, cs.AI, and cs.DS

Abstract: Tokenization is the process of encoding strings into tokens of a fixed vocabulary size, and is widely utilized in Natural Language Processing applications. The leading tokenization algorithm today is Byte-Pair Encoding (BPE), which formulates the tokenization problem as a compression problem and tackles it by performing sequences of merges. In this work, we formulate tokenization as an optimization objective, show that it is NP-hard via a simple reduction from vertex cover, and propose a polynomial-time greedy algorithm GreedTok. Our formulation naturally relaxes to the well-studied weighted maximum coverage problem which has a simple $(1 - 1/e)$-approximation algorithm GreedWMC. Through empirical evaluations on real-world corpora, we show that GreedTok outperforms BPE and Unigram on compression and achieves a covering score comparable to GreedWMC. Finally, our extensive pre-training for two transformer-based LLMs with 1 billion parameters, comparing the choices of BPE and GreedTok as the tokenizer, shows that GreedTok achieves a lower bit per byte even when we control for either the total dataset proportion or total training tokens.

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets