{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QPHARSYS3VOCEPALAPJHB7QCDO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"089dd70b63b41cdc7bbbaa58a7262a82620822489bcfaf8bc7210ae7984d6036","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-08T21:18:11Z","title_canon_sha256":"1bd1f93b8351828478db6d3e41302600e52a0a76868f4d0625e26d714dd438a0"},"schema_version":"1.0","source":{"id":"2010.04261","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.04261","created_at":"2026-07-05T05:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"2010.04261v6","created_at":"2026-07-05T05:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.04261","created_at":"2026-07-05T05:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"QPHARSYS3VOC","created_at":"2026-07-05T05:09:03Z"},{"alias_kind":"pith_short_16","alias_value":"QPHARSYS3VOCEPAL","created_at":"2026-07-05T05:09:03Z"},{"alias_kind":"pith_short_8","alias_value":"QPHARSYS","created_at":"2026-07-05T05:09:03Z"}],"graph_snapshots":[{"event_id":"sha256:d9a98d4bcdb9faed9542ff430125041d14e08a6539a6e84c99a57e3834b9ec3f","target":"graph","created_at":"2026-07-05T05:09:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.04261/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. In this paper, we propose a decoupling conjecture that decomposes the layer-wise Hessians of a network as the Kronecker product of two smaller matrices. We can analyze the properties of these smaller matrices and prove the structure of top eigenspace random 2-layer networks. The decoupling conjecture has several other interesting implications - top eigenspaces for different models have surprisingly high overlap, and top eigenvector","authors_text":"Annie Wang, Chenwei Wu, Rong Ge, Xingyu Zhu, Yikai Wu","cross_cats":["cs.NE","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-08T21:18:11Z","title":"Dissecting Hessian: Understanding Common Structure of Hessian in Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.04261","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:79f9ed12e6c8c7af13165fa49adad3d46c5e8cb2b7ad21b501322f13c770a4bf","target":"record","created_at":"2026-07-05T05:09:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"089dd70b63b41cdc7bbbaa58a7262a82620822489bcfaf8bc7210ae7984d6036","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-08T21:18:11Z","title_canon_sha256":"1bd1f93b8351828478db6d3e41302600e52a0a76868f4d0625e26d714dd438a0"},"schema_version":"1.0","source":{"id":"2010.04261","kind":"arxiv","version":6}},"canonical_sha256":"83ce08cb12dd5c223c0b03d270fe021b97c0c008c3c8b13f55523fcceb116d09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ce08cb12dd5c223c0b03d270fe021b97c0c008c3c8b13f55523fcceb116d09","first_computed_at":"2026-07-05T05:09:03.733130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:09:03.733130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qoTpyYWqj56netMcqZZW7kNXVGDnidTrDtxG4hIkkLAY6gh6SjG6y+rnnopwwZdkEHM6Wq1j3I4yX74WVn8lAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:09:03.733570Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.04261","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f9ed12e6c8c7af13165fa49adad3d46c5e8cb2b7ad21b501322f13c770a4bf","sha256:d9a98d4bcdb9faed9542ff430125041d14e08a6539a6e84c99a57e3834b9ec3f"],"state_sha256":"ca88d12b490dfc1f0c55e3137811a3c6f7dd5de533ec1b9a2ded13aa0392970b"}