{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZQZF52ZQ75IGS7HHJROWEY3H7K","short_pith_number":"pith:ZQZF52ZQ","canonical_record":{"source":{"id":"1805.11917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-30T12:21:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f647759132b4605f9b0ac108d4e8f14bf76683b8de03a214c56cf42025bf4e42","abstract_canon_sha256":"322465062b3d2bfa66df862db9d5cda4b1dcdf5d8c78a9fca434130888b2d4f3"},"schema_version":"1.0"},"canonical_sha256":"cc325eeb30ff50697ce74c5d626367faa8050c8e73a3f1a3865b91be05ed9eb1","source":{"kind":"arxiv","id":"1805.11917","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11917","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11917v2","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11917","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZQZF52ZQ75IG","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZQZF52ZQ75IGS7HH","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZQZF52ZQ","created_at":"2026-07-05T02:23:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZQZF52ZQ75IGS7HHJROWEY3H7K","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-30T12:21:17Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f647759132b4605f9b0ac108d4e8f14bf76683b8de03a214c56cf42025bf4e42","abstract_canon_sha256":"322465062b3d2bfa66df862db9d5cda4b1dcdf5d8c78a9fca434130888b2d4f3"},"schema_version":"1.0"},"canonical_sha256":"cc325eeb30ff50697ce74c5d626367faa8050c8e73a3f1a3865b91be05ed9eb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:23:55.316065Z","signature_b64":"QsP69VNA7of7lM6tatwqvn+QsbrlZno4JXZkAWJ/4qx3T9ofW3tEctZgXjhvbEjBAXVRsaSsqWLfU5BiQ+ESCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc325eeb30ff50697ce74c5d626367faa8050c8e73a3f1a3865b91be05ed9eb1","last_reissued_at":"2026-07-05T02:23:55.315719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:23:55.315719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11917","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":"2026-07-05T02:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5DKX4JPJ1KLueKPlrrL/wc059xFY0ZRXsyoEyDwUvXzafyRTRyFMchqQvOxMC5nH/iHA5I/n+kJrXOgDgSzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:51:51.628887Z"},"content_sha256":"8a351bd22cf4dbcf8af92b9185aac1886c3e362c4d937035b48dfec4f1729a06","schema_version":"1.0","event_id":"sha256:8a351bd22cf4dbcf8af92b9185aac1886c3e362c4d937035b48dfec4f1729a06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZQZF52ZQ75IGS7HHJROWEY3H7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dynamics of Learning: A Random Matrix Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Romain Couillet, Zhenyu Liao","submitted_at":"2018-05-30T12:21:17Z","abstract_excerpt":"Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we introduce a random matrix-based framework to analyze the learning dynamics of a single-layer linear network on a binary classification problem, for data of simultaneously large dimension and size, trained by gradient descent. Our results provide rich insights into common questions in neural nets, such as overfitting, early stopping and the initialization of traini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11917","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/1805.11917/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":"2026-07-05T02:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GV/YAL8Rs6a3M7X74N5ht2UOGW++oa4dvLzNgo37YUJHa/7g6JnjmoUfW6FIsr7qOn1aLIONMVWjNTEASL3jBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:51:51.629677Z"},"content_sha256":"e6a5228c33849d772da5abd8eb1cb07524c96f0d737b9f620dadb1dfa9fc8ce6","schema_version":"1.0","event_id":"sha256:e6a5228c33849d772da5abd8eb1cb07524c96f0d737b9f620dadb1dfa9fc8ce6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/bundle.json","state_url":"https://pith.science/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/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":"2026-08-16T20:51:51Z","links":{"resolver":"https://pith.science/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K","bundle":"https://pith.science/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/bundle.json","state":"https://pith.science/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQZF52ZQ75IGS7HHJROWEY3H7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZQZF52ZQ75IGS7HHJROWEY3H7K","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":"322465062b3d2bfa66df862db9d5cda4b1dcdf5d8c78a9fca434130888b2d4f3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-30T12:21:17Z","title_canon_sha256":"f647759132b4605f9b0ac108d4e8f14bf76683b8de03a214c56cf42025bf4e42"},"schema_version":"1.0","source":{"id":"1805.11917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11917","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11917v2","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11917","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZQZF52ZQ75IG","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZQZF52ZQ75IGS7HH","created_at":"2026-07-05T02:23:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZQZF52ZQ","created_at":"2026-07-05T02:23:55Z"}],"graph_snapshots":[{"event_id":"sha256:e6a5228c33849d772da5abd8eb1cb07524c96f0d737b9f620dadb1dfa9fc8ce6","target":"graph","created_at":"2026-07-05T02:23:55Z","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/1805.11917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we introduce a random matrix-based framework to analyze the learning dynamics of a single-layer linear network on a binary classification problem, for data of simultaneously large dimension and size, trained by gradient descent. Our results provide rich insights into common questions in neural nets, such as overfitting, early stopping and the initialization of traini","authors_text":"Romain Couillet, Zhenyu Liao","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-30T12:21:17Z","title":"The Dynamics of Learning: A Random Matrix Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11917","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":"sha256:8a351bd22cf4dbcf8af92b9185aac1886c3e362c4d937035b48dfec4f1729a06","target":"record","created_at":"2026-07-05T02:23:55Z","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":"322465062b3d2bfa66df862db9d5cda4b1dcdf5d8c78a9fca434130888b2d4f3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-05-30T12:21:17Z","title_canon_sha256":"f647759132b4605f9b0ac108d4e8f14bf76683b8de03a214c56cf42025bf4e42"},"schema_version":"1.0","source":{"id":"1805.11917","kind":"arxiv","version":2}},"canonical_sha256":"cc325eeb30ff50697ce74c5d626367faa8050c8e73a3f1a3865b91be05ed9eb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc325eeb30ff50697ce74c5d626367faa8050c8e73a3f1a3865b91be05ed9eb1","first_computed_at":"2026-07-05T02:23:55.315719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:23:55.315719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QsP69VNA7of7lM6tatwqvn+QsbrlZno4JXZkAWJ/4qx3T9ofW3tEctZgXjhvbEjBAXVRsaSsqWLfU5BiQ+ESCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:23:55.316065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a351bd22cf4dbcf8af92b9185aac1886c3e362c4d937035b48dfec4f1729a06","sha256:e6a5228c33849d772da5abd8eb1cb07524c96f0d737b9f620dadb1dfa9fc8ce6"],"state_sha256":"0731f15d30f19f3f80365d84cdadc4aa5d70193ad6b86f5b90a5ea038f95bf1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQkkFQGn+X4ljlfvi3SqzqlVxikDrmkXnDIP4UHKNvw13O9YyziL+02zUVuRMaC64j0aMCLjw63MU/Wkzh2OAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:51:51.636709Z","bundle_sha256":"fc5df7902675068784606c81112f1b1af30e22d057cae513a7053d534943d2d6"}}