{"paper":{"title":"Higher-order Linear Attention","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Higher-order Linear Attention captures second-order interactions in linear time with a constant-size state.","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Quanquan Gu, Yifan Zhang, Zhen Qin","submitted_at":"2025-10-31T07:54:37Z","abstract_excerpt":"The quadratic cost of scaled dot-product attention is a central obstacle to scaling autoregressive language models to long contexts. Linear-time attention and State Space Models (SSMs) provide scalable alternatives but are typically restricted to first-order or kernel-based approximations, which can limit expressivity. We introduce Higher-order Linear Attention (HLA), a causal, streaming mechanism that realizes higher interactions via compact prefix sufficient statistics. In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materia"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any n × n matrices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That compact prefix sufficient statistics exist and suffice to realize the desired higher-order interactions while preserving the causal streaming property and exact equivalence to the serial recurrence.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Higher-order Linear Attention realizes second-order and higher interactions in linear-time causal attention via constant-size state and associative scans.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Higher-order Linear Attention captures second-order interactions in linear time with a constant-size state.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b13b8529c27f9929f91f1b543ae1d504bee2857e21d372f730569860e4c16b4d"},"source":{"id":"2510.27258","kind":"arxiv","version":3},"verdict":{"id":"0d980761-c643-48e4-83af-7b4b47fcaebc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T03:03:06.024190Z","strongest_claim":"In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any n × n matrices.","one_line_summary":"Higher-order Linear Attention realizes second-order and higher interactions in linear-time causal attention via constant-size state and associative scans.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That compact prefix sufficient statistics exist and suffice to realize the desired higher-order interactions while preserving the causal streaming property and exact equivalence to the serial recurrence.","pith_extraction_headline":"Higher-order Linear Attention captures second-order interactions in linear time with a constant-size state."},"references":{"count":18,"sample":[{"doi":"","year":null,"title":"Titans: Learning to Memorize at Test Time","work_id":"fb2b7625-b733-43cb-af52-00b0a31a8d7f","ref_index":1,"cited_arxiv_id":"2501.00663","is_internal_anchor":true},{"doi":"","year":null,"title":"Atlas: Learning to optimally memorize the context at test time","work_id":"88ad83a5-1a41-49a6-a975-2d9374634987","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Rethinking Attention with Performers","work_id":"4c26d308-8b72-4a98-8e73-950617a75f50","ref_index":3,"cited_arxiv_id":"2009.14794","is_internal_anchor":true},{"doi":"","year":null,"title":"Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality","work_id":"d8eba076-0449-4f6a-aae1-5a7260677f0f","ref_index":4,"cited_arxiv_id":"2405.21060","is_internal_anchor":true},{"doi":"","year":null,"title":"Mamba: Linear-Time Sequence Modeling with Selective State Spaces","work_id":"4ee75248-1199-492c-a52f-6661e0f4adff","ref_index":5,"cited_arxiv_id":"2312.00752","is_internal_anchor":true}],"resolved_work":18,"snapshot_sha256":"aa8e2f50389f1003f8e05673391b7eabf3afaa849c25e915a2c32bab6e3caa49","internal_anchors":12},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e460d43a0a4ab87bf36a224d74c352b5064764644a4d0f0254bdd95e8dad4fd5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}