{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DFFTQOG7N56PZVB3IPEH6ITOKN","short_pith_number":"pith:DFFTQOG7","canonical_record":{"source":{"id":"2602.07697","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-07T20:47:32Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"41cc0c702dadbdf5de03f7be4823cf0eae0b01da2e760614fb218292206762e4","abstract_canon_sha256":"cb72da50ed75cc6282245af384bc5a055ec51982b1552d2403a97b958c1365ea"},"schema_version":"1.0"},"canonical_sha256":"194b3838df6f7cfcd43b43c87f226e5371f4254180826ec6236d2bba481fbeed","source":{"kind":"arxiv","id":"2602.07697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.07697","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2602.07697v2","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.07697","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"DFFTQOG7N56P","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"DFFTQOG7N56PZVB3","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"DFFTQOG7","created_at":"2026-05-25T02:02:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DFFTQOG7N56PZVB3IPEH6ITOKN","target":"record","payload":{"canonical_record":{"source":{"id":"2602.07697","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-07T20:47:32Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"41cc0c702dadbdf5de03f7be4823cf0eae0b01da2e760614fb218292206762e4","abstract_canon_sha256":"cb72da50ed75cc6282245af384bc5a055ec51982b1552d2403a97b958c1365ea"},"schema_version":"1.0"},"canonical_sha256":"194b3838df6f7cfcd43b43c87f226e5371f4254180826ec6236d2bba481fbeed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:13.195763Z","signature_b64":"EV+Pp4pasz2AoWQyvvKXaHj04AZ7HheaLYowZVuHCeIvwZnADq0lJL2ptW2RaBLQj53slDX7n7r4N64KGfE1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"194b3838df6f7cfcd43b43c87f226e5371f4254180826ec6236d2bba481fbeed","last_reissued_at":"2026-05-25T02:02:13.194828Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:13.194828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.07697","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvrT5Te1r4flnFnZ18KcZm9UMWyTmLDx33snr70LpivUSElaEEe6wj/m2zCOn9Qw0hZ8+0/J8PjIz1gxhyksAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:34:45.232285Z"},"content_sha256":"506f388e59ac25607fb3ec4cd6a4e31ee99f999f73f6013e710eaebba471a038","schema_version":"1.0","event_id":"sha256:506f388e59ac25607fb3ec4cd6a4e31ee99f999f73f6013e710eaebba471a038"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DFFTQOG7N56PZVB3IPEH6ITOKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Infinite Width and Depth Limits of Predictive Coding Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"cs.LG","authors_text":"El Mehdi Achour, Francesco Innocenti, Rafal Bogacz","submitted_at":"2026-02-07T20:47:32Z","abstract_excerpt":"Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.07697","kind":"arxiv","version":2},"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/2602.07697/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywyst+r2/i7yLDBVBHoTDBCVvdYdJRcG8qBbRawZwjM7VqscikyAxdXbdbfstixS8xYMzIq3dLinG1cSX48BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:34:45.233095Z"},"content_sha256":"079e6372b49ecc991e3e0b2002acc290e849558d939982ab54aa045f837aa20f","schema_version":"1.0","event_id":"sha256:079e6372b49ecc991e3e0b2002acc290e849558d939982ab54aa045f837aa20f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/bundle.json","state_url":"https://pith.science/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T19:34:45Z","links":{"resolver":"https://pith.science/pith/DFFTQOG7N56PZVB3IPEH6ITOKN","bundle":"https://pith.science/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/bundle.json","state":"https://pith.science/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFFTQOG7N56PZVB3IPEH6ITOKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFFTQOG7N56PZVB3IPEH6ITOKN","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":"cb72da50ed75cc6282245af384bc5a055ec51982b1552d2403a97b958c1365ea","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-07T20:47:32Z","title_canon_sha256":"41cc0c702dadbdf5de03f7be4823cf0eae0b01da2e760614fb218292206762e4"},"schema_version":"1.0","source":{"id":"2602.07697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.07697","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2602.07697v2","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.07697","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"DFFTQOG7N56P","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"DFFTQOG7N56PZVB3","created_at":"2026-05-25T02:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"DFFTQOG7","created_at":"2026-05-25T02:02:13Z"}],"graph_snapshots":[{"event_id":"sha256:079e6372b49ecc991e3e0b2002acc290e849558d939982ab54aa045f837aa20f","target":"graph","created_at":"2026-05-25T02:02:13Z","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/2602.07697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is ","authors_text":"El Mehdi Achour, Francesco Innocenti, Rafal Bogacz","cross_cats":["cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-07T20:47:32Z","title":"On the Infinite Width and Depth Limits of Predictive Coding Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.07697","kind":"arxiv","version":2},"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":"sha256:506f388e59ac25607fb3ec4cd6a4e31ee99f999f73f6013e710eaebba471a038","target":"record","created_at":"2026-05-25T02:02:13Z","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":"cb72da50ed75cc6282245af384bc5a055ec51982b1552d2403a97b958c1365ea","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-07T20:47:32Z","title_canon_sha256":"41cc0c702dadbdf5de03f7be4823cf0eae0b01da2e760614fb218292206762e4"},"schema_version":"1.0","source":{"id":"2602.07697","kind":"arxiv","version":2}},"canonical_sha256":"194b3838df6f7cfcd43b43c87f226e5371f4254180826ec6236d2bba481fbeed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"194b3838df6f7cfcd43b43c87f226e5371f4254180826ec6236d2bba481fbeed","first_computed_at":"2026-05-25T02:02:13.194828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:13.194828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EV+Pp4pasz2AoWQyvvKXaHj04AZ7HheaLYowZVuHCeIvwZnADq0lJL2ptW2RaBLQj53slDX7n7r4N64KGfE1Dw==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:13.195763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.07697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:506f388e59ac25607fb3ec4cd6a4e31ee99f999f73f6013e710eaebba471a038","sha256:079e6372b49ecc991e3e0b2002acc290e849558d939982ab54aa045f837aa20f"],"state_sha256":"5470fe5aa6befa45900e5b458204c6e7093d13e31de6634a2305b0d4aa2deaff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0TiA/xOtkwaTo0olBv+uQI279ZuCfgmLpQQVIdSiqGcxzKtY2CreePQ/isnMOOz9cmWQI1rlhPOhB4eP0OWGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T19:34:45.237700Z","bundle_sha256":"1e285984b17aba7ffa70a184ed86ac650756cb591e8b946dcf35abb72ba363ca"}}