{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-formal-perspective-on-byte-pair-encoding","title":"A Formal Perspective on Byte-Pair Encoding","arxiv_id":"2306.16837","date":"2023-06-29","proceeding":null,"authors":["Vilém Zouhar","Clara Meister","Juan Luis Gastaldi","Li Du","Tim Vieira","Mrinmaya Sachan","Ryan Cotterell"],"abstract":"Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a $\\frac{1}{{\\sigma(\\boldsymbol{\\mu}^\\star)}}(1-e^{-{\\sigma(\\boldsymbol{\\mu}^\\star)}})$-approximation of an optimal merge sequence, where ${\\sigma(\\boldsymbol{\\mu}^\\star)}$ is the total backward curvature with respect to the optimal merge sequence $\\boldsymbol{\\mu}^\\star$. Empirically the lower bound of the approximation is $\\approx 0.37$. We provide a faster implementation of BPE which improves the runtime complexity from $\\mathcal{O}\\left(N M\\right)$ to $\\mathcal{O}\\left(N \\log M\\right)$, where $N$ is the sequence length and $M$ is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.","url_abs":"https://arxiv.org/abs/2306.16837v3","url_pdf":"https://arxiv.org/pdf/2306.16837v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-formal-perspective-on-byte-pair-encoding","repo_url":"https://github.com/zouharvi/formal-bpe","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[{"method_slug":"bpe","method_name":"BPE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2306.16837","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}