{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4TI6RN3HTC7TZDKIEBZYHHAXT7","short_pith_number":"pith:4TI6RN3H","canonical_record":{"source":{"id":"2405.14689","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T15:25:56Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"8fd17340eeba402fb9602b3a4fdf1fbdcc339c7e75f3e4d1c24e01b742f50057","abstract_canon_sha256":"4c01bf2afb072cb7fe763169b5cc8635ee9c2e5bbee46b2afb0efaf3519c41f2"},"schema_version":"1.0"},"canonical_sha256":"e4d1e8b76798bf3c8d482073839c179fcec6a2807c54d45698941dc537b76027","source":{"kind":"arxiv","id":"2405.14689","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14689","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14689v4","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14689","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"4TI6RN3HTC7T","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TI6RN3HTC7TZDKI","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TI6RN3H","created_at":"2026-07-05T10:11:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4TI6RN3HTC7TZDKIEBZYHHAXT7","target":"record","payload":{"canonical_record":{"source":{"id":"2405.14689","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T15:25:56Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"8fd17340eeba402fb9602b3a4fdf1fbdcc339c7e75f3e4d1c24e01b742f50057","abstract_canon_sha256":"4c01bf2afb072cb7fe763169b5cc8635ee9c2e5bbee46b2afb0efaf3519c41f2"},"schema_version":"1.0"},"canonical_sha256":"e4d1e8b76798bf3c8d482073839c179fcec6a2807c54d45698941dc537b76027","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:58.844170Z","signature_b64":"7KdeJWbqMRSAn/WcmEwqiTxCEfrMj1fdHrGw5e+maY3mnnosKL7SS7bk7TJG+m9Va8kFezDTlmJWls+QutLaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4d1e8b76798bf3c8d482073839c179fcec6a2807c54d45698941dc537b76027","last_reissued_at":"2026-07-05T10:11:58.843582Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:58.843582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.14689","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":"2026-07-05T10:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRyfFsTKm1o4xhsMWTai0fbg6s5gDf9IU4axC+2WA1EVMyBpKEK7jcvAqGGmY7ZhTfvsOcf7Oeph06O+kOHACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:17:36.178230Z"},"content_sha256":"b883df7cf3eb5563521d4fc16ed46aa691511aaf0a7a1295e11bf1b857c8a96e","schema_version":"1.0","event_id":"sha256:b883df7cf3eb5563521d4fc16ed46aa691511aaf0a7a1295e11bf1b857c8a96e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4TI6RN3HTC7TZDKIEBZYHHAXT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cascade of phase transitions in the training of Energy-based models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"primary_cat":"cs.LG","authors_text":"Aur\\'elien Decelle, Beatriz Seoane, Dimitrios Bachtis, Giulio Biroli","submitted_at":"2024-05-23T15:25:56Z","abstract_excerpt":"In this paper, we investigate the feature encoding process in a prototypical energy-based generative model, the Restricted Boltzmann Machine (RBM). We start with an analytical investigation using simplified architectures and data structures, and end with numerical analysis of real trainings on real datasets. Our study tracks the evolution of the model's weight matrix through its singular value decomposition, revealing a series of phase transitions associated to a progressive learning of the principal modes of the empirical probability distribution. The model first learns the center of mass of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14689","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/2405.14689/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":"2026-07-05T10:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/JtAaiAjr1fDajrAS/ZvUONQUfc3BNGf4J8qfVA4OdqI07JOsf+0+mZ0hmNwCC6r9xJ4gcU01wmTKoKCCg6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:17:36.178737Z"},"content_sha256":"8f784b23b8412148fdc81326d0e1c5e8815fd1526297314c05a532f03b1de5ce","schema_version":"1.0","event_id":"sha256:8f784b23b8412148fdc81326d0e1c5e8815fd1526297314c05a532f03b1de5ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/bundle.json","state_url":"https://pith.science/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/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":"2026-08-08T16:17:36Z","links":{"resolver":"https://pith.science/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7","bundle":"https://pith.science/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/bundle.json","state":"https://pith.science/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TI6RN3HTC7TZDKIEBZYHHAXT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4TI6RN3HTC7TZDKIEBZYHHAXT7","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":"4c01bf2afb072cb7fe763169b5cc8635ee9c2e5bbee46b2afb0efaf3519c41f2","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T15:25:56Z","title_canon_sha256":"8fd17340eeba402fb9602b3a4fdf1fbdcc339c7e75f3e4d1c24e01b742f50057"},"schema_version":"1.0","source":{"id":"2405.14689","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14689","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14689v4","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14689","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"4TI6RN3HTC7T","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TI6RN3HTC7TZDKI","created_at":"2026-07-05T10:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TI6RN3H","created_at":"2026-07-05T10:11:58Z"}],"graph_snapshots":[{"event_id":"sha256:8f784b23b8412148fdc81326d0e1c5e8815fd1526297314c05a532f03b1de5ce","target":"graph","created_at":"2026-07-05T10:11:58Z","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/2405.14689/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the feature encoding process in a prototypical energy-based generative model, the Restricted Boltzmann Machine (RBM). We start with an analytical investigation using simplified architectures and data structures, and end with numerical analysis of real trainings on real datasets. Our study tracks the evolution of the model's weight matrix through its singular value decomposition, revealing a series of phase transitions associated to a progressive learning of the principal modes of the empirical probability distribution. The model first learns the center of mass of ","authors_text":"Aur\\'elien Decelle, Beatriz Seoane, Dimitrios Bachtis, Giulio Biroli","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T15:25:56Z","title":"Cascade of phase transitions in the training of Energy-based models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14689","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:b883df7cf3eb5563521d4fc16ed46aa691511aaf0a7a1295e11bf1b857c8a96e","target":"record","created_at":"2026-07-05T10:11:58Z","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":"4c01bf2afb072cb7fe763169b5cc8635ee9c2e5bbee46b2afb0efaf3519c41f2","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T15:25:56Z","title_canon_sha256":"8fd17340eeba402fb9602b3a4fdf1fbdcc339c7e75f3e4d1c24e01b742f50057"},"schema_version":"1.0","source":{"id":"2405.14689","kind":"arxiv","version":4}},"canonical_sha256":"e4d1e8b76798bf3c8d482073839c179fcec6a2807c54d45698941dc537b76027","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4d1e8b76798bf3c8d482073839c179fcec6a2807c54d45698941dc537b76027","first_computed_at":"2026-07-05T10:11:58.843582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:58.843582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KdeJWbqMRSAn/WcmEwqiTxCEfrMj1fdHrGw5e+maY3mnnosKL7SS7bk7TJG+m9Va8kFezDTlmJWls+QutLaDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:58.844170Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.14689","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b883df7cf3eb5563521d4fc16ed46aa691511aaf0a7a1295e11bf1b857c8a96e","sha256:8f784b23b8412148fdc81326d0e1c5e8815fd1526297314c05a532f03b1de5ce"],"state_sha256":"2788162299c508a2fef8ffc18010cbf57872be7511b114151ea51677c157b673"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9AVinBR5as0C6kqYhjMbz0KJxv/vGsYphtp9Wzv3sHjdNlieAOFqqgA+B3TTPTIDoDn0u5guum/qGXyEoZRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:17:36.184271Z","bundle_sha256":"df2c2bcadd418e51dd5c9c6301cf8047d1d9bc4f1457efafb922b65906ca397b"}}