{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ESBTB6ASF2MJHMYRZRYBV2PAPV","short_pith_number":"pith:ESBTB6AS","schema_version":"1.0","canonical_sha256":"248330f8122e9893b311cc701ae9e07d7d1f84d6d839185911a8bbc0e57a5ba2","source":{"kind":"arxiv","id":"2606.31536","version":1},"attestation_state":"computed","paper":{"title":"Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.LG","authors_text":"Kung-Ming Lan","submitted_at":"2026-06-30T11:50:52Z","abstract_excerpt":"As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory. In classical deep learning, increasing model capacity typically risks overfitting. However, this study advances a counter-intuitive paradigm: unstructured contemporary QML architectures suffer from a profound state of quantum underfitting, driven by the \"expressivity-trainability paradox.\" We demonstrate that the vast Hilbert space capacity of Parameterized Quantum Circuits (PQCs)"},"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":"2606.31536","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-30T11:50:52Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"b4905ded538a317b1277162e0c091ddc54e7589d9969285ee72ae7557aa5ecf5","abstract_canon_sha256":"bf21ff8464dd7c2a77b57a0f98b638ed7f5c5f80061e6193f70c89388be82a9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:06.409329Z","signature_b64":"XgE2sFnxV+i8NR3bReGTtXvaev914nAA7qfFGqupow0Hd606Z6NrmxVA1TRxssi8RKAn8PLiBzgF5OZhPMOwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"248330f8122e9893b311cc701ae9e07d7d1f84d6d839185911a8bbc0e57a5ba2","last_reissued_at":"2026-07-01T01:18:06.408918Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:06.408918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.LG","authors_text":"Kung-Ming Lan","submitted_at":"2026-06-30T11:50:52Z","abstract_excerpt":"As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory. In classical deep learning, increasing model capacity typically risks overfitting. However, this study advances a counter-intuitive paradigm: unstructured contemporary QML architectures suffer from a profound state of quantum underfitting, driven by the \"expressivity-trainability paradox.\" We demonstrate that the vast Hilbert space capacity of Parameterized Quantum Circuits (PQCs)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31536","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/2606.31536/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":"2606.31536","created_at":"2026-07-01T01:18:06.408973+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31536v1","created_at":"2026-07-01T01:18:06.408973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31536","created_at":"2026-07-01T01:18:06.408973+00:00"},{"alias_kind":"pith_short_12","alias_value":"ESBTB6ASF2MJ","created_at":"2026-07-01T01:18:06.408973+00:00"},{"alias_kind":"pith_short_16","alias_value":"ESBTB6ASF2MJHMYR","created_at":"2026-07-01T01:18:06.408973+00:00"},{"alias_kind":"pith_short_8","alias_value":"ESBTB6AS","created_at":"2026-07-01T01:18:06.408973+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/ESBTB6ASF2MJHMYRZRYBV2PAPV","json":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV.json","graph_json":"https://pith.science/api/pith-number/ESBTB6ASF2MJHMYRZRYBV2PAPV/graph.json","events_json":"https://pith.science/api/pith-number/ESBTB6ASF2MJHMYRZRYBV2PAPV/events.json","paper":"https://pith.science/paper/ESBTB6AS"},"agent_actions":{"view_html":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV","download_json":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV.json","view_paper":"https://pith.science/paper/ESBTB6AS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31536&json=true","fetch_graph":"https://pith.science/api/pith-number/ESBTB6ASF2MJHMYRZRYBV2PAPV/graph.json","fetch_events":"https://pith.science/api/pith-number/ESBTB6ASF2MJHMYRZRYBV2PAPV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV/action/storage_attestation","attest_author":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV/action/author_attestation","sign_citation":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV/action/citation_signature","submit_replication":"https://pith.science/pith/ESBTB6ASF2MJHMYRZRYBV2PAPV/action/replication_record"}},"created_at":"2026-07-01T01:18:06.408973+00:00","updated_at":"2026-07-01T01:18:06.408973+00:00"}