{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:OKRYSYK7JORKC54EL4TAOR4HHG","short_pith_number":"pith:OKRYSYK7","schema_version":"1.0","canonical_sha256":"72a389615f4ba2a177845f2607478739b9d1e163d88d3ed468910a01515a22a0","source":{"kind":"arxiv","id":"2606.17522","version":1},"attestation_state":"computed","paper":{"title":"An expressivity analysis of hierarchical modelling in deep transformers via bounded-depth grammars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Pramod Thebe, Qiang Qu, Sakshi Khachariya, Tongliang Liu, Vinoth Nandakumar","submitted_at":"2026-06-16T05:02:13Z","abstract_excerpt":"Deep neural networks are widely believed to derive their expressive power from their ability to form \\textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers. In language modeling, \\textbf{transformers} have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies. While this intuition has shaped model design, there remains a lack of rigorous theoretical work demonstrating \\textbf{how} deep transformers represent such hierarchical struc"},"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":"2606.17522","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-06-16T05:02:13Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8072525ffc79e2de23cd4830a386d905f6c716992017e5aaa21035027dd87212","abstract_canon_sha256":"d5502372545d86d31fa9b16a8c31e6af5f0be7e53e88bd6082cdbcc5479615e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:15.071977Z","signature_b64":"f+8VgxlM6x1Nzev98fcC8pDhbKtu1tYAMTdV8oNzb/kWhoNJdCe5rv/kB5eG8vE0eBWpGzmrfIzgL+KDRNwWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72a389615f4ba2a177845f2607478739b9d1e163d88d3ed468910a01515a22a0","last_reissued_at":"2026-06-19T16:10:15.071595Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:15.071595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An expressivity analysis of hierarchical modelling in deep transformers via bounded-depth grammars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Pramod Thebe, Qiang Qu, Sakshi Khachariya, Tongliang Liu, Vinoth Nandakumar","submitted_at":"2026-06-16T05:02:13Z","abstract_excerpt":"Deep neural networks are widely believed to derive their expressive power from their ability to form \\textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers. In language modeling, \\textbf{transformers} have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies. While this intuition has shaped model design, there remains a lack of rigorous theoretical work demonstrating \\textbf{how} deep transformers represent such hierarchical struc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17522","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/2606.17522/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":"2606.17522","created_at":"2026-06-19T16:10:15.071655+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.17522v1","created_at":"2026-06-19T16:10:15.071655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17522","created_at":"2026-06-19T16:10:15.071655+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKRYSYK7JORK","created_at":"2026-06-19T16:10:15.071655+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKRYSYK7JORKC54E","created_at":"2026-06-19T16:10:15.071655+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKRYSYK7","created_at":"2026-06-19T16:10:15.071655+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/OKRYSYK7JORKC54EL4TAOR4HHG","json":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG.json","graph_json":"https://pith.science/api/pith-number/OKRYSYK7JORKC54EL4TAOR4HHG/graph.json","events_json":"https://pith.science/api/pith-number/OKRYSYK7JORKC54EL4TAOR4HHG/events.json","paper":"https://pith.science/paper/OKRYSYK7"},"agent_actions":{"view_html":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG","download_json":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG.json","view_paper":"https://pith.science/paper/OKRYSYK7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.17522&json=true","fetch_graph":"https://pith.science/api/pith-number/OKRYSYK7JORKC54EL4TAOR4HHG/graph.json","fetch_events":"https://pith.science/api/pith-number/OKRYSYK7JORKC54EL4TAOR4HHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG/action/storage_attestation","attest_author":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG/action/author_attestation","sign_citation":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG/action/citation_signature","submit_replication":"https://pith.science/pith/OKRYSYK7JORKC54EL4TAOR4HHG/action/replication_record"}},"created_at":"2026-06-19T16:10:15.071655+00:00","updated_at":"2026-06-19T16:10:15.071655+00:00"}