{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4XXAZL77BCLQ6E43CPOY35OAJI","short_pith_number":"pith:4XXAZL77","schema_version":"1.0","canonical_sha256":"e5ee0cafff08970f139b13dd8df5c04a2bf1df26bb2791a15b13f7fcdd8a1061","source":{"kind":"arxiv","id":"2509.07963","version":2},"attestation_state":"computed","paper":{"title":"Customizing the Inductive Biases of Softmax Attention using Structured Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andres Potapczynski, Andrew Gordon Wilson, Noah Amsel, Sanae Lotfi, Shikai Qiu, Yilun Kuang","submitted_at":"2025-09-09T17:50:58Z","abstract_excerpt":"The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient stru"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.07963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-09T17:50:58Z","cross_cats_sorted":[],"title_canon_sha256":"b5da63fe9d41cb4f20bf1d16827eb87dd9bad49c76cd411b1ed17b8e1ba593b4","abstract_canon_sha256":"6b467c98292f3b11657b0bf20eb0955e4855866792c633aa6904cf73efb7137c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:12.162175Z","signature_b64":"FPjwdsnal1GcasFxoKZMzvnfhtlc+entH9wzwpEjmM6iDlTdKNfiynK15p98pIhIGRn7mY4YY6WrAaiucPhPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5ee0cafff08970f139b13dd8df5c04a2bf1df26bb2791a15b13f7fcdd8a1061","last_reissued_at":"2026-06-04T01:08:12.161602Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:12.161602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Customizing the Inductive Biases of Softmax Attention using Structured Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andres Potapczynski, Andrew Gordon Wilson, Noah Amsel, Sanae Lotfi, Shikai Qiu, Yilun Kuang","submitted_at":"2025-09-09T17:50:58Z","abstract_excerpt":"The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07963","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/2509.07963/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.07963","created_at":"2026-06-04T01:08:12.161672+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07963v2","created_at":"2026-06-04T01:08:12.161672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07963","created_at":"2026-06-04T01:08:12.161672+00:00"},{"alias_kind":"pith_short_12","alias_value":"4XXAZL77BCLQ","created_at":"2026-06-04T01:08:12.161672+00:00"},{"alias_kind":"pith_short_16","alias_value":"4XXAZL77BCLQ6E43","created_at":"2026-06-04T01:08:12.161672+00:00"},{"alias_kind":"pith_short_8","alias_value":"4XXAZL77","created_at":"2026-06-04T01:08:12.161672+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI","json":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI.json","graph_json":"https://pith.science/api/pith-number/4XXAZL77BCLQ6E43CPOY35OAJI/graph.json","events_json":"https://pith.science/api/pith-number/4XXAZL77BCLQ6E43CPOY35OAJI/events.json","paper":"https://pith.science/paper/4XXAZL77"},"agent_actions":{"view_html":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI","download_json":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI.json","view_paper":"https://pith.science/paper/4XXAZL77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07963&json=true","fetch_graph":"https://pith.science/api/pith-number/4XXAZL77BCLQ6E43CPOY35OAJI/graph.json","fetch_events":"https://pith.science/api/pith-number/4XXAZL77BCLQ6E43CPOY35OAJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI/action/storage_attestation","attest_author":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI/action/author_attestation","sign_citation":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI/action/citation_signature","submit_replication":"https://pith.science/pith/4XXAZL77BCLQ6E43CPOY35OAJI/action/replication_record"}},"created_at":"2026-06-04T01:08:12.161672+00:00","updated_at":"2026-06-04T01:08:12.161672+00:00"}