{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Z5ZGCFCMN3RQCM2EGTW4EZOSZP","short_pith_number":"pith:Z5ZGCFCM","schema_version":"1.0","canonical_sha256":"cf7261144c6ee301334434edc265d2cbed36635533f60e43a7c26414fa92738f","source":{"kind":"arxiv","id":"2412.09925","version":2},"attestation_state":"computed","paper":{"title":"Simulating Hard Attention Using Soft Attention","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL","cs.FL"],"primary_cat":"cs.LG","authors_text":"Andy Yang, Dana Angluin, David Chiang, Lena Strobl","submitted_at":"2024-12-13T07:27:42Z","abstract_excerpt":"We study conditions under which transformers using soft attention can simulate hard attention, that is, effectively focus all attention on a subset of positions. First, we examine several subclasses of languages recognized by hard-attention transformers, which can be defined in variants of linear temporal logic. We demonstrate how soft-attention transformers can compute formulas of these logics using unbounded positional embeddings or temperature scaling. Second, we demonstrate how temperature scaling allows softmax transformers to simulate general hard-attention transformers, using a temperat"},"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":"2412.09925","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-13T07:27:42Z","cross_cats_sorted":["cs.CL","cs.FL"],"title_canon_sha256":"efb6a33d7710093794edf0ce015b730b14840926517898396a3655b5d084e651","abstract_canon_sha256":"11b2268fbca557a440d6e045f3ad2aaa3ac674f982d8805a91385ad94fbe3438"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:22.663909Z","signature_b64":"27/CL6DiCo9fUELopgYbrykQDa0W9lsGytDAT9YRX1ASyNmOLM4tX4b9h9yraKqmnkkfUxHwRCM3iIDEmV+4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf7261144c6ee301334434edc265d2cbed36635533f60e43a7c26414fa92738f","last_reissued_at":"2026-07-05T11:27:22.663362Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:22.663362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simulating Hard Attention Using Soft Attention","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL","cs.FL"],"primary_cat":"cs.LG","authors_text":"Andy Yang, Dana Angluin, David Chiang, Lena Strobl","submitted_at":"2024-12-13T07:27:42Z","abstract_excerpt":"We study conditions under which transformers using soft attention can simulate hard attention, that is, effectively focus all attention on a subset of positions. First, we examine several subclasses of languages recognized by hard-attention transformers, which can be defined in variants of linear temporal logic. We demonstrate how soft-attention transformers can compute formulas of these logics using unbounded positional embeddings or temperature scaling. Second, we demonstrate how temperature scaling allows softmax transformers to simulate general hard-attention transformers, using a temperat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.09925","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/2412.09925/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":"2412.09925","created_at":"2026-07-05T11:27:22.663448+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.09925v2","created_at":"2026-07-05T11:27:22.663448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.09925","created_at":"2026-07-05T11:27:22.663448+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z5ZGCFCMN3RQ","created_at":"2026-07-05T11:27:22.663448+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z5ZGCFCMN3RQCM2E","created_at":"2026-07-05T11:27:22.663448+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z5ZGCFCM","created_at":"2026-07-05T11:27:22.663448+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/Z5ZGCFCMN3RQCM2EGTW4EZOSZP","json":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP.json","graph_json":"https://pith.science/api/pith-number/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/graph.json","events_json":"https://pith.science/api/pith-number/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/events.json","paper":"https://pith.science/paper/Z5ZGCFCM"},"agent_actions":{"view_html":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP","download_json":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP.json","view_paper":"https://pith.science/paper/Z5ZGCFCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.09925&json=true","fetch_graph":"https://pith.science/api/pith-number/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/graph.json","fetch_events":"https://pith.science/api/pith-number/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/action/storage_attestation","attest_author":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/action/author_attestation","sign_citation":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/action/citation_signature","submit_replication":"https://pith.science/pith/Z5ZGCFCMN3RQCM2EGTW4EZOSZP/action/replication_record"}},"created_at":"2026-07-05T11:27:22.663448+00:00","updated_at":"2026-07-05T11:27:22.663448+00:00"}