{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KUIV43KVG6RPI7XZTFEO4L6O2V","short_pith_number":"pith:KUIV43KV","canonical_record":{"source":{"id":"2312.05705","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-09T23:13:32Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4dc785090d04ae403bbdf03f232762c451b93278873f8e1099d8fe17a619bcc4","abstract_canon_sha256":"1b8c1480e16f7bb88285ed960bc9a42e6cb612a6620a3501478ab8a4fc7888af"},"schema_version":"1.0"},"canonical_sha256":"55115e6d5537a2f47ef99948ee2fced56941e4ce0a811d4d3f401e0d472eb071","source":{"kind":"arxiv","id":"2312.05705","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.05705","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2312.05705v4","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.05705","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"KUIV43KVG6RP","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUIV43KVG6RPI7XZ","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUIV43KV","created_at":"2026-07-05T08:47:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KUIV43KVG6RPI7XZTFEO4L6O2V","target":"record","payload":{"canonical_record":{"source":{"id":"2312.05705","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-09T23:13:32Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"4dc785090d04ae403bbdf03f232762c451b93278873f8e1099d8fe17a619bcc4","abstract_canon_sha256":"1b8c1480e16f7bb88285ed960bc9a42e6cb612a6620a3501478ab8a4fc7888af"},"schema_version":"1.0"},"canonical_sha256":"55115e6d5537a2f47ef99948ee2fced56941e4ce0a811d4d3f401e0d472eb071","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:47:09.186045Z","signature_b64":"PM60MbgDLUwEykWYk0ixVXEfjX6V30gPw53arVDLQyFBwqpYdRUPOPgFbtWgJrxdDELGJ4p+ojsN77ogIHSmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55115e6d5537a2f47ef99948ee2fced56941e4ce0a811d4d3f401e0d472eb071","last_reissued_at":"2026-07-05T08:47:09.185305Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:47:09.185305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.05705","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQXTtUqGFe0gaeo8/tLivjKrtq/qAKNXH3sgaVbWwWG8TnU6COPBAL3mKY9HBkD0HBsM9z5F7ce9og04SjMvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:58:17.507518Z"},"content_sha256":"fc2b83cd330bfafa8914d57272127cf96bdc55061c5ef2afcc7e2cb9f7d742a5","schema_version":"1.0","event_id":"sha256:fc2b83cd330bfafa8914d57272127cf96bdc55061c5ef2afcc7e2cb9f7d742a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KUIV43KVG6RPI7XZTFEO4L6O2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Agustinus Kristiadi, Alireza Makhzani, Felix Dangel, Kirill Neklyudov, Richard E. Turner, Runa Eschenhagen, Wu Lin","submitted_at":"2023-12-09T23:13:32Z","abstract_excerpt":"Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-effi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.05705","kind":"arxiv","version":4},"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/2312.05705/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":"2026-07-05T08:47:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBI5GHQCjjQTWYASYjLRnPlj/K0kWZrOEWLK7oJbJuq/H/Oe4FaNiXwTU7aPLNONMyMb0c746jSB+Qa7ojfaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:58:17.508022Z"},"content_sha256":"34945a29c71d0e8dbde4af99658e830954cd54e0dd5fc65e7d484835955715c2","schema_version":"1.0","event_id":"sha256:34945a29c71d0e8dbde4af99658e830954cd54e0dd5fc65e7d484835955715c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/bundle.json","state_url":"https://pith.science/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/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":"2026-08-05T08:58:17Z","links":{"resolver":"https://pith.science/pith/KUIV43KVG6RPI7XZTFEO4L6O2V","bundle":"https://pith.science/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/bundle.json","state":"https://pith.science/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUIV43KVG6RPI7XZTFEO4L6O2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KUIV43KVG6RPI7XZTFEO4L6O2V","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":"1b8c1480e16f7bb88285ed960bc9a42e6cb612a6620a3501478ab8a4fc7888af","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-09T23:13:32Z","title_canon_sha256":"4dc785090d04ae403bbdf03f232762c451b93278873f8e1099d8fe17a619bcc4"},"schema_version":"1.0","source":{"id":"2312.05705","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.05705","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2312.05705v4","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.05705","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"KUIV43KVG6RP","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUIV43KVG6RPI7XZ","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUIV43KV","created_at":"2026-07-05T08:47:09Z"}],"graph_snapshots":[{"event_id":"sha256:34945a29c71d0e8dbde4af99658e830954cd54e0dd5fc65e7d484835955715c2","target":"graph","created_at":"2026-07-05T08:47:09Z","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/2312.05705/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-effi","authors_text":"Agustinus Kristiadi, Alireza Makhzani, Felix Dangel, Kirill Neklyudov, Richard E. Turner, Runa Eschenhagen, Wu Lin","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-09T23:13:32Z","title":"Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.05705","kind":"arxiv","version":4},"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:fc2b83cd330bfafa8914d57272127cf96bdc55061c5ef2afcc7e2cb9f7d742a5","target":"record","created_at":"2026-07-05T08:47:09Z","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":"1b8c1480e16f7bb88285ed960bc9a42e6cb612a6620a3501478ab8a4fc7888af","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-09T23:13:32Z","title_canon_sha256":"4dc785090d04ae403bbdf03f232762c451b93278873f8e1099d8fe17a619bcc4"},"schema_version":"1.0","source":{"id":"2312.05705","kind":"arxiv","version":4}},"canonical_sha256":"55115e6d5537a2f47ef99948ee2fced56941e4ce0a811d4d3f401e0d472eb071","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55115e6d5537a2f47ef99948ee2fced56941e4ce0a811d4d3f401e0d472eb071","first_computed_at":"2026-07-05T08:47:09.185305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:09.185305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PM60MbgDLUwEykWYk0ixVXEfjX6V30gPw53arVDLQyFBwqpYdRUPOPgFbtWgJrxdDELGJ4p+ojsN77ogIHSmAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:09.186045Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.05705","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc2b83cd330bfafa8914d57272127cf96bdc55061c5ef2afcc7e2cb9f7d742a5","sha256:34945a29c71d0e8dbde4af99658e830954cd54e0dd5fc65e7d484835955715c2"],"state_sha256":"aa8812ff771e61333c9d675a621b7119d072f5be2a15f154d2fe796f718408ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFpo0Ak//21D4hJXE6SJIHVy57PNHRu6/k0zX6Jvtj4jGkTWqhsZS1KU8KW9uRTC0AE5lUFdZsziG1g/3XgYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T08:58:17.511856Z","bundle_sha256":"c8ceca84623ce39178e4cdcfdb96b857b21f90ddc2a15bc83cbb9d9567c0f94b"}}