{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:B7OXAZOPRUUFM3LCFZKYNH5NPY","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":"5b2ed07b21d15bd2d47fdd0337c1a4c5ab8a5c9598e8dd9393dff0a42bccd477","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-01T15:23:49Z","title_canon_sha256":"20ee09f68863fd76255319ae0bc28d03d28ffe1ac091bf0c9e643b346be2aaad"},"schema_version":"1.0","source":{"id":"2209.00530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.00530","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"2209.00530v1","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.00530","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"B7OXAZOPRUUF","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_16","alias_value":"B7OXAZOPRUUFM3LC","created_at":"2026-07-05T04:53:51Z"},{"alias_kind":"pith_short_8","alias_value":"B7OXAZOP","created_at":"2026-07-05T04:53:51Z"}],"graph_snapshots":[{"event_id":"sha256:0a5228f840c30d18c93e49871505b7f2c61b67ef96e19ccc740f634d6bcfe2c2","target":"graph","created_at":"2026-07-05T04:53:51Z","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/2209.00530/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Equilibrium propagation (EP) is an alternative to backpropagation (BP) that allows the training of deep neural networks with local learning rules. It thus provides a compelling framework for training neuromorphic systems and understanding learning in neurobiology. However, EP requires infinitesimal teaching signals, thereby limiting its applicability in noisy physical systems. Moreover, the algorithm requires separate temporal phases and has not been applied to large-scale problems. Here we address these issues by extending EP to holomorphic networks. We show analytically that this extension n","authors_text":"Axel Laborieux, Friedemann Zenke","cross_cats":["cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-01T15:23:49Z","title":"Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00530","kind":"arxiv","version":1},"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:c2a9e2578e06f929e0972439450882e1c2f63f8baaca6be7581952f424db46ca","target":"record","created_at":"2026-07-05T04:53:51Z","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":"5b2ed07b21d15bd2d47fdd0337c1a4c5ab8a5c9598e8dd9393dff0a42bccd477","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-09-01T15:23:49Z","title_canon_sha256":"20ee09f68863fd76255319ae0bc28d03d28ffe1ac091bf0c9e643b346be2aaad"},"schema_version":"1.0","source":{"id":"2209.00530","kind":"arxiv","version":1}},"canonical_sha256":"0fdd7065cf8d28566d622e55869fad7e345c8327d255dfca84d4a8e5da564218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fdd7065cf8d28566d622e55869fad7e345c8327d255dfca84d4a8e5da564218","first_computed_at":"2026-07-05T04:53:51.054956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:51.054956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JEMhdgWAG8+pfytNg/hvuth02xh/Jo+HoScN95S5kWXGkoVOFj+YdzfBy/Iu9o0+Nu4PnkThvBmbZ5vUgWpXAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:51.055344Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.00530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2a9e2578e06f929e0972439450882e1c2f63f8baaca6be7581952f424db46ca","sha256:0a5228f840c30d18c93e49871505b7f2c61b67ef96e19ccc740f634d6bcfe2c2"],"state_sha256":"5089ba806a96941aaff6809a42e3fbc43b2b98df0f7eb45be7e0ab1d29da6829"}