{"paper":{"title":"Understanding Addition and Subtraction in Transformers","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.CL"],"primary_cat":"cs.LG","authors_text":"Clement Neo, Fazl Barez, Philip Quirke","submitted_at":"2024-02-04T21:33:18Z","abstract_excerpt":"We use integer addition and subtraction as a controlled, exactly-solvable testbed for what can be said with confidence about the algorithm a low-loss transformer implements - logically and mechanically. We train small transformers (2-3 layers) from scratch, find the edge cases they fail (long carry and borrow cascades), and enrich the training data with them; most resulting models reach >$99.999% accuracy on 5-15 digit problems in under an hour, solving cascades such as 555555555+444444448=+1000000003. Interpretability analysis of these accurate models - not an a-priori guess - surfaces the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02619","kind":"arxiv","version":11},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.02619/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}