{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:DQYWWOUBTVSYR3NF7URHCF6ZKQ","short_pith_number":"pith:DQYWWOUB","schema_version":"1.0","canonical_sha256":"1c316b3a819d6588eda5fd227117d95400dd308431cd1d02ed769edc67e40ffb","source":{"kind":"arxiv","id":"2405.16391","version":3},"attestation_state":"computed","paper":{"title":"When does compositional structure yield compositional generalization? A kernel theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"cs.LG","authors_text":"Kim Stachenfeld, Samuel Lippl","submitted_at":"2024-05-26T00:50:11Z","abstract_excerpt":"Compositional generalization (the ability to respond correctly to novel combinations of familiar components) is thought to be a cornerstone of intelligent behavior. Compositionally structured (e.g. disentangled) representations support this ability; however, the conditions under which they are sufficient for the emergence of compositional generalization remain unclear. To address this gap, we present a theory of compositional generalization in kernel models with fixed, compositionally structured representations. This provides a tractable framework for characterizing the impact of training data"},"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":"2405.16391","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T00:50:11Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"800d8c5b93bcece41e6cea9ec2806b3fa7a37ab9c0c74e2dd5270c5ad670141f","abstract_canon_sha256":"ea122ac14fb29f307d17abadbc862d4ca14c64247284bba3b14fee46609390e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:52.504787Z","signature_b64":"J888s++PrFVd00QME4ArbDj2EO32c1vNzb2COol7Rw6rZ1wZonLyEG9e2mjxRTv7NPGFmidp+iv7k4DyDjn1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c316b3a819d6588eda5fd227117d95400dd308431cd1d02ed769edc67e40ffb","last_reissued_at":"2026-07-05T10:45:52.504301Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:52.504301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When does compositional structure yield compositional generalization? A kernel theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"cs.LG","authors_text":"Kim Stachenfeld, Samuel Lippl","submitted_at":"2024-05-26T00:50:11Z","abstract_excerpt":"Compositional generalization (the ability to respond correctly to novel combinations of familiar components) is thought to be a cornerstone of intelligent behavior. Compositionally structured (e.g. disentangled) representations support this ability; however, the conditions under which they are sufficient for the emergence of compositional generalization remain unclear. To address this gap, we present a theory of compositional generalization in kernel models with fixed, compositionally structured representations. This provides a tractable framework for characterizing the impact of training data"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16391","kind":"arxiv","version":3},"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/2405.16391/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":"2405.16391","created_at":"2026-07-05T10:45:52.504365+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.16391v3","created_at":"2026-07-05T10:45:52.504365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16391","created_at":"2026-07-05T10:45:52.504365+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQYWWOUBTVSY","created_at":"2026-07-05T10:45:52.504365+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQYWWOUBTVSYR3NF","created_at":"2026-07-05T10:45:52.504365+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQYWWOUB","created_at":"2026-07-05T10:45:52.504365+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.18797","citing_title":"Compositional Generalization via Forced Rendering of Disentangled Latents","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ","json":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ.json","graph_json":"https://pith.science/api/pith-number/DQYWWOUBTVSYR3NF7URHCF6ZKQ/graph.json","events_json":"https://pith.science/api/pith-number/DQYWWOUBTVSYR3NF7URHCF6ZKQ/events.json","paper":"https://pith.science/paper/DQYWWOUB"},"agent_actions":{"view_html":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ","download_json":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ.json","view_paper":"https://pith.science/paper/DQYWWOUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.16391&json=true","fetch_graph":"https://pith.science/api/pith-number/DQYWWOUBTVSYR3NF7URHCF6ZKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/DQYWWOUBTVSYR3NF7URHCF6ZKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ/action/storage_attestation","attest_author":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ/action/author_attestation","sign_citation":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ/action/citation_signature","submit_replication":"https://pith.science/pith/DQYWWOUBTVSYR3NF7URHCF6ZKQ/action/replication_record"}},"created_at":"2026-07-05T10:45:52.504365+00:00","updated_at":"2026-07-05T10:45:52.504365+00:00"}