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Tokenization complexity: BPE approximation proven NP-hard

A new research paper explores the computational complexity of tokenization algorithms like Byte-Pair Encoding (BPE). The study proves that unless P=NP, no efficient algorithm can approximate the optimal number of merges for BPE on binary strings within a factor of $c n / ext{log } n$. For merges that can skip occurrences, a simple algorithm achieves $O(n / ext{log log } n)$, and for unary datasets, both tokenization problems are strongly NP-complete. AI

IMPACT Understanding tokenization complexity is crucial for optimizing the efficiency of large language models.

RANK_REASON Academic paper detailing theoretical computer science research on tokenization algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.CL →

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Tokenization complexity: BPE approximation proven NP-hard

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Academic paper detailing theoretical computer science research on tokenization algorithms. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.CL TIER_1 English(EN) · Kundan Baliga, Aiden Xie, Aditya Byju ·

    Pair-Merge Tokenisation Is Hard to Approximate on Binary Strings and Strongly NP-Hard on Unary Datasets

    arXiv:2611.13568v1 Announce Type: cross Abstract: Tokenisers such as Byte-Pair Encoding (BPE) shorten text by repeatedly merging an adjacent pair of symbols into a new one; fewer tokens mean less computation. We ask whether an efficient algorithm can choose $k$ merges that leave …