{"paper":{"title":"Minimalist Softmax Attention Provably Learns Constrained Boolean Functions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Han Liu, Jerry Yao-Chieh Hu, Maojiang Su, Xiwen Zhang, Zhao Song","submitted_at":"2025-05-26T05:33:26Z","abstract_excerpt":"We study the computational limits of learning $k$-bit Boolean functions (specifically, $\\mathrm{AND}$, $\\mathrm{OR}$, and their noisy variants), using a minimalist single-head softmax-attention mechanism, where $k=\\Theta(d)$ relevant bits are selected from $d$ inputs. We show that these simple $\\mathrm{AND}$ and $\\mathrm{OR}$ functions are unsolvable with a single-head softmax-attention mechanism alone. However, with teacher forcing, the same minimalist attention is capable of solving them. These findings offer two key insights: Architecturally, solving these Boolean tasks requires only minima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19531","kind":"arxiv","version":1},"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/2505.19531/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"}