{"paper":{"title":"Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","cs.PF"],"primary_cat":"cs.LG","authors_text":"Gaetan Hains, Lenore Mullin","submitted_at":"2026-06-05T14:44:49Z","abstract_excerpt":"The attention mechanism is the dominant computational bottleneck in modern transformer-based AI. Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck.\n  We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) that eliminates all intermediate arrays -- includ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07713","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/2606.07713/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"}