{"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/regress-don-t-guess-a-regression-like-loss-on","title":"Regress, Don't Guess -- A Regression-like Loss on Number Tokens for Language Models","arxiv_id":"2411.02083","date":"2024-11-04","proceeding":null,"authors":["Jonas Zausinger","Lars Pennig","Anamarija Kozina","Sean Sdahl","Julian Sikora","Adrian Dendorfer","Timofey Kuznetsov","Mohamad Hagog","Nina Wiedemann","Kacper Chlodny","Vincent Limbach","Anna Ketteler","Thorben Prein","Vishwa Mohan Singh","Michael Morris Danziger","Jannis Born"],"abstract":"While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving quantitative reasoning, especially arithmetic. One fundamental limitation is the nature of the Cross Entropy loss, which assumes a nominal scale and thus cannot convey proximity between generated number tokens. In response, we here present a regression-like loss that operates purely on token level. Our proposed Number Token Loss (NTL) comes in two flavors and minimizes either the Lp norm or the Wasserstein distance between the numerical values of the real and predicted number tokens. NTL can easily be added to any language model and extend the Cross Entropy objective during training without runtime overhead. We evaluate the proposed scheme on various mathematical datasets and find that it consistently improves performance in math-related tasks. In a direct comparison on a regression task, we find that NTL can match the performance of a regression head, despite operating on token level. Finally, we scale NTL up to 3B parameter models and observe improved performance, demonstrating its potential for seamless integration into LLMs. We hope that this work can inspire LLM developers to improve their pretraining objectives. The code is available via: https://tum-ai.github.io/number-token-loss/","url_abs":"https://arxiv.org/abs/2411.02083v2","url_pdf":"https://arxiv.org/pdf/2411.02083v2.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":"regress-don-t-guess-a-regression-like-loss-on","repo_url":"https://github.com/tum-ai/number-token-loss","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"inductive-bias","task_name":"Inductive Bias"},{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"math","task_name":"Math"},{"task_slug":"text-generation","task_name":"Text Generation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"adafactor","method_name":"Adafactor"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"glu","method_name":"Gated Linear Unit"},{"method_slug":"inverse-square-root-schedule","method_name":"Inverse Square Root Schedule"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"sentencepiece","method_name":"SentencePiece"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"t5","method_name":"T5"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2411.02083","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2411.02083"}},"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":"deterministic:regex_extraction","url":"https://github.com/ai4sd/numbertoken-loss","reach":{"status":"gone","observed_at":"2026-09-17","how":"tree_404+repo_404"}},{"provenance":"deterministic:regex_extraction","url":"https://github.com/tum-ai/number-token-loss","reach":null}],"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":0,"samples":[{"code_sha256_prefix":"062547c2683b3da4","entry":"NumberTokenLoss","repo":"tum-ai/number-token-loss","repo_kind":"official","path":"src/ntl/loss_functions/base_number_token_loss.py","file_url":"https://github.com/tum-ai/number-token-loss/blob/HEAD/src/ntl/loss_functions/base_number_token_loss.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"062547c2683b3da4"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}