{"paper":{"title":"Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.NT"],"primary_cat":"cs.AI","authors_text":"Alessandro Breccia, Federica Gerace, Gabriele Sicuro, Marco Lippi, Pierluigi Contucci","submitted_at":"2025-12-01T16:51:38Z","abstract_excerpt":"We study whether a transformer network can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $\\mathbb{N}\\mathscr{T}$ defines an arithmetic text with measurable statistical structure. A transformer network (the GPT-2 architecture) is trained from scratch on the first $10^{11}$ elements and evaluated on Next-Token and masked-word prediction tasks, with a Hidden Markov Model as baseline and a scaling analysis over context window, dataset size, vocabulary size a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01870","kind":"arxiv","version":2},"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/2512.01870/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"}