{"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/xval-a-continuous-number-encoding-for-large","title":"xVal: A Continuous Numerical Tokenization for Scientific Language Models","arxiv_id":"2310.02989","date":"2023-10-04","proceeding":null,"authors":["Siavash Golkar","Mariel Pettee","Michael Eickenberg","Alberto Bietti","Miles Cranmer","Geraud Krawezik","Francois Lanusse","Michael McCabe","Ruben Ohana","Liam Parker","Bruno Régaldo-Saint Blancard","Tiberiu Tesileanu","Kyunghyun Cho","Shirley Ho"],"abstract":"Due in part to their discontinuous and discrete default encodings for numbers, Large Language Models (LLMs) have not yet been commonly used to process numerically-dense scientific datasets. Rendering datasets as text, however, could help aggregate diverse and multi-modal scientific data into a single training corpus, thereby potentially facilitating the development of foundation models for science. In this work, we introduce xVal, a strategy for continuously tokenizing numbers within language models that results in a more appropriate inductive bias for scientific applications. By training specially-modified language models from scratch on a variety of scientific datasets formatted as text, we find that xVal generally outperforms other common numerical tokenization strategies on metrics including out-of-distribution generalization and computational efficiency.","url_abs":"https://arxiv.org/abs/2310.02989v2","url_pdf":"https://arxiv.org/pdf/2310.02989v2.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":"xval-a-continuous-number-encoding-for-large","repo_url":"https://github.com/PolymathicAI/xVal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"xval-a-continuous-number-encoding-for-large","repo_url":"https://github.com/lucidrains/iTransformer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"inductive-bias","task_name":"Inductive Bias"},{"task_slug":"out-of-distribution-generalization","task_name":"Out-of-Distribution Generalization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2310.02989","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.02989"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/PolymathicAI/xVal","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lucidrains/iTransformer","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"bd2cadf558f541c9","entry":"Numformer","repo":"PolymathicAI/xVal","repo_kind":"official","path":"xval/numformer.py","file_url":"https://github.com/PolymathicAI/xVal/blob/HEAD/xval/numformer.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"bd2cadf558f541c9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}