{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BAUYJYRK3J6534XKZYJMR344MJ","short_pith_number":"pith:BAUYJYRK","canonical_record":{"source":{"id":"2605.19483","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T07:34:58Z","cross_cats_sorted":[],"title_canon_sha256":"5701b345a418de83245c4326d0c6a6b774f3111606849b8959519f38a1ada6eb","abstract_canon_sha256":"08b68e3b021fd749041f390022f66dc4b392d14bd22b276774c5c2bbdd50a9b5"},"schema_version":"1.0"},"canonical_sha256":"082984e22ada7dddf2eace12c8ef9c6251fa3cc588711fb9b70d5b7127443cff","source":{"kind":"arxiv","id":"2605.19483","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19483","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19483v1","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19483","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"BAUYJYRK3J65","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"BAUYJYRK3J6534XK","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"BAUYJYRK","created_at":"2026-05-20T01:05:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BAUYJYRK3J6534XKZYJMR344MJ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19483","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T07:34:58Z","cross_cats_sorted":[],"title_canon_sha256":"5701b345a418de83245c4326d0c6a6b774f3111606849b8959519f38a1ada6eb","abstract_canon_sha256":"08b68e3b021fd749041f390022f66dc4b392d14bd22b276774c5c2bbdd50a9b5"},"schema_version":"1.0"},"canonical_sha256":"082984e22ada7dddf2eace12c8ef9c6251fa3cc588711fb9b70d5b7127443cff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:47.978885Z","signature_b64":"VlPWdKg4AM6K5t7MaiuInrNHvzpTUGs+WB5U2I2agSWCyymlelglG/WDf9c5FbrEoR7kY6vuWBcD+akAlE1nDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"082984e22ada7dddf2eace12c8ef9c6251fa3cc588711fb9b70d5b7127443cff","last_reissued_at":"2026-05-20T01:05:47.978210Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:47.978210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19483","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufMp/Ief4V2em4oO0K9AajBWOGJpaLxOifmzlp+FqPRnSq5R/tJHjIfs8hQxi99YGDxJpq5CKtgXHycTIcsmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:13:12.252148Z"},"content_sha256":"18f2c45e4ddcc602fa63864e7421b0af4d2e6adcd3f475827b4d51d8072eb2dc","schema_version":"1.0","event_id":"sha256:18f2c45e4ddcc602fa63864e7421b0af4d2e6adcd3f475827b4d51d8072eb2dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BAUYJYRK3J6534XKZYJMR344MJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adynamical systems view of training generativemodels and the memorization phenomenon","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Chiranjib Bhattacharya, Siva Athreya, Vivek S. Borkar","submitted_at":"2026-05-19T07:34:58Z","abstract_excerpt":"Using recent works of one of the authors (VSB) on collapse in generative models and two time scale dynamics in stochastic gradient descent in high dimensions, we give a system theoretic explanation of the memorization phenomenon in generative models. This relies purely on the dynamic aspects of the training phase. Specifically, we use a result of Austin [2016] to motivate a stylized model for the loss function for stochastic gradient descent (SGD) wherein the loss function has a strong dependence on some variables and weak dependence on the rest in a precise sense. This naturally leads to two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19483","kind":"arxiv","version":1},"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/2605.19483/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":"2026-05-20T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbT9AWBz55mQoHFLdzu53i4I/M/Rl9MFJ7362wlAbTo1ew2/7TOUYpNnz66rbsqOJ9qD8uq3PRyEelBohGCoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:13:12.252555Z"},"content_sha256":"bd161114914568ee2c5823aefdac1a178612fa6d91e601d84a346c44e3a8bbbe","schema_version":"1.0","event_id":"sha256:bd161114914568ee2c5823aefdac1a178612fa6d91e601d84a346c44e3a8bbbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAUYJYRK3J6534XKZYJMR344MJ/bundle.json","state_url":"https://pith.science/pith/BAUYJYRK3J6534XKZYJMR344MJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAUYJYRK3J6534XKZYJMR344MJ/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":"2026-06-02T23:13:12Z","links":{"resolver":"https://pith.science/pith/BAUYJYRK3J6534XKZYJMR344MJ","bundle":"https://pith.science/pith/BAUYJYRK3J6534XKZYJMR344MJ/bundle.json","state":"https://pith.science/pith/BAUYJYRK3J6534XKZYJMR344MJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAUYJYRK3J6534XKZYJMR344MJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BAUYJYRK3J6534XKZYJMR344MJ","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":"08b68e3b021fd749041f390022f66dc4b392d14bd22b276774c5c2bbdd50a9b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T07:34:58Z","title_canon_sha256":"5701b345a418de83245c4326d0c6a6b774f3111606849b8959519f38a1ada6eb"},"schema_version":"1.0","source":{"id":"2605.19483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19483","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19483v1","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19483","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"BAUYJYRK3J65","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"BAUYJYRK3J6534XK","created_at":"2026-05-20T01:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"BAUYJYRK","created_at":"2026-05-20T01:05:47Z"}],"graph_snapshots":[{"event_id":"sha256:bd161114914568ee2c5823aefdac1a178612fa6d91e601d84a346c44e3a8bbbe","target":"graph","created_at":"2026-05-20T01:05:47Z","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/2605.19483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using recent works of one of the authors (VSB) on collapse in generative models and two time scale dynamics in stochastic gradient descent in high dimensions, we give a system theoretic explanation of the memorization phenomenon in generative models. This relies purely on the dynamic aspects of the training phase. Specifically, we use a result of Austin [2016] to motivate a stylized model for the loss function for stochastic gradient descent (SGD) wherein the loss function has a strong dependence on some variables and weak dependence on the rest in a precise sense. This naturally leads to two ","authors_text":"Chiranjib Bhattacharya, Siva Athreya, Vivek S. Borkar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T07:34:58Z","title":"Adynamical systems view of training generativemodels and the memorization phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19483","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":"sha256:18f2c45e4ddcc602fa63864e7421b0af4d2e6adcd3f475827b4d51d8072eb2dc","target":"record","created_at":"2026-05-20T01:05:47Z","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":"08b68e3b021fd749041f390022f66dc4b392d14bd22b276774c5c2bbdd50a9b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T07:34:58Z","title_canon_sha256":"5701b345a418de83245c4326d0c6a6b774f3111606849b8959519f38a1ada6eb"},"schema_version":"1.0","source":{"id":"2605.19483","kind":"arxiv","version":1}},"canonical_sha256":"082984e22ada7dddf2eace12c8ef9c6251fa3cc588711fb9b70d5b7127443cff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"082984e22ada7dddf2eace12c8ef9c6251fa3cc588711fb9b70d5b7127443cff","first_computed_at":"2026-05-20T01:05:47.978210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:47.978210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VlPWdKg4AM6K5t7MaiuInrNHvzpTUGs+WB5U2I2agSWCyymlelglG/WDf9c5FbrEoR7kY6vuWBcD+akAlE1nDQ==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:47.978885Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f2c45e4ddcc602fa63864e7421b0af4d2e6adcd3f475827b4d51d8072eb2dc","sha256:bd161114914568ee2c5823aefdac1a178612fa6d91e601d84a346c44e3a8bbbe"],"state_sha256":"896b955e0d7a9f3a72032458ca02e49ee35b7afd977528c139d4991f8b938017"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvnzGAqF0dm8WCcwzkmoAMn9ClM7dBVZxsFXqvv3KR4RgREMcWcshzHtqgwr2vU+taqbKQpKK81ryTqhAWohAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:13:12.254646Z","bundle_sha256":"a66220ffda75a022c2992821321022abd3d98a9d3da09a85106bd3368ae7f720"}}