{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KOWPLRCBK43YJYCG3ABOV5GQOX","short_pith_number":"pith:KOWPLRCB","canonical_record":{"source":{"id":"2411.15945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-24T18:20:05Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"title_canon_sha256":"3dea7a8151381abaa7dd83c781c52f57d1082bb46d389f593b9f3ad3dc8bec9c","abstract_canon_sha256":"02bb99e0960ff7ae1094f642d2ea778d0a5383eb7282a54aa23cab6b9a8f74f7"},"schema_version":"1.0"},"canonical_sha256":"53acf5c441573784e046d802eaf4d075da3cbbc43338390c27462aa21d3ae6a3","source":{"kind":"arxiv","id":"2411.15945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15945","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15945v1","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15945","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_12","alias_value":"KOWPLRCBK43Y","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_16","alias_value":"KOWPLRCBK43YJYCG","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_8","alias_value":"KOWPLRCB","created_at":"2026-07-05T09:39:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KOWPLRCBK43YJYCG3ABOV5GQOX","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-24T18:20:05Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"title_canon_sha256":"3dea7a8151381abaa7dd83c781c52f57d1082bb46d389f593b9f3ad3dc8bec9c","abstract_canon_sha256":"02bb99e0960ff7ae1094f642d2ea778d0a5383eb7282a54aa23cab6b9a8f74f7"},"schema_version":"1.0"},"canonical_sha256":"53acf5c441573784e046d802eaf4d075da3cbbc43338390c27462aa21d3ae6a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:44.155404Z","signature_b64":"6ReqxNryYsS81BZop9WxIM2W/wjMefCasThwMwUHH/LCJAejSbVPnxhy2rixxZnB7iBqcg7J1GlKe2Cu5Xw3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53acf5c441573784e046d802eaf4d075da3cbbc43338390c27462aa21d3ae6a3","last_reissued_at":"2026-07-05T09:39:44.154916Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:44.154916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15945","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":"2026-07-05T09:39:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z93SmPfAQjrB2VULMtwbx9Df7UBsAx3Kr6RaJDw8kJWe3meYjVnVPdf84Tg5pok0m/K2oP3Xt6nQ9AGhn2lgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:39:57.859979Z"},"content_sha256":"dffdf56124ce9e76a44b2191ed14a515e8fe919479de960457397cf53781de07","schema_version":"1.0","event_id":"sha256:dffdf56124ce9e76a44b2191ed14a515e8fe919479de960457397cf53781de07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KOWPLRCBK43YJYCG3ABOV5GQOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding Machine Learning Paradigms through the Lens of Statistical Thermodynamics: A tutorial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"primary_cat":"cs.LG","authors_text":"Star (Xinxin) Liu","submitted_at":"2024-11-24T18:20:05Z","abstract_excerpt":"This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial delves into advanced techniques like entropy, free energy, and variational inference which are utilized in machine learning, illustrating their significant contributions to model efficiency and robustness. By bridging these scientific disciplines, we aspire to inspire newer methodologies in researches, demonstrating how an in-depth comprehension of physical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15945","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/2411.15945/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":"2026-07-05T09:39:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDyNh627a85q1+rPYQ7L6yqnH+o8r3qjrsZ3WrjGNci16YA/r0PVtfpVpAac6EYaMs8EkY/9+/qywV6IW9OQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:39:57.860578Z"},"content_sha256":"be4d33d152eeb7c780dfc36b970c140c4863ded93a79369e0a0c6002707823b7","schema_version":"1.0","event_id":"sha256:be4d33d152eeb7c780dfc36b970c140c4863ded93a79369e0a0c6002707823b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/bundle.json","state_url":"https://pith.science/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/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":"2026-08-13T01:39:57Z","links":{"resolver":"https://pith.science/pith/KOWPLRCBK43YJYCG3ABOV5GQOX","bundle":"https://pith.science/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/bundle.json","state":"https://pith.science/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOWPLRCBK43YJYCG3ABOV5GQOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KOWPLRCBK43YJYCG3ABOV5GQOX","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":"02bb99e0960ff7ae1094f642d2ea778d0a5383eb7282a54aa23cab6b9a8f74f7","cross_cats_sorted":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-24T18:20:05Z","title_canon_sha256":"3dea7a8151381abaa7dd83c781c52f57d1082bb46d389f593b9f3ad3dc8bec9c"},"schema_version":"1.0","source":{"id":"2411.15945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15945","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15945v1","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15945","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_12","alias_value":"KOWPLRCBK43Y","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_16","alias_value":"KOWPLRCBK43YJYCG","created_at":"2026-07-05T09:39:44Z"},{"alias_kind":"pith_short_8","alias_value":"KOWPLRCB","created_at":"2026-07-05T09:39:44Z"}],"graph_snapshots":[{"event_id":"sha256:be4d33d152eeb7c780dfc36b970c140c4863ded93a79369e0a0c6002707823b7","target":"graph","created_at":"2026-07-05T09:39:44Z","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/2411.15945/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial delves into advanced techniques like entropy, free energy, and variational inference which are utilized in machine learning, illustrating their significant contributions to model efficiency and robustness. By bridging these scientific disciplines, we aspire to inspire newer methodologies in researches, demonstrating how an in-depth comprehension of physical ","authors_text":"Star (Xinxin) Liu","cross_cats":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-24T18:20:05Z","title":"Understanding Machine Learning Paradigms through the Lens of Statistical Thermodynamics: A tutorial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15945","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:dffdf56124ce9e76a44b2191ed14a515e8fe919479de960457397cf53781de07","target":"record","created_at":"2026-07-05T09:39:44Z","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":"02bb99e0960ff7ae1094f642d2ea778d0a5383eb7282a54aa23cab6b9a8f74f7","cross_cats_sorted":["cond-mat.mtrl-sci","math.ST","physics.chem-ph","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-24T18:20:05Z","title_canon_sha256":"3dea7a8151381abaa7dd83c781c52f57d1082bb46d389f593b9f3ad3dc8bec9c"},"schema_version":"1.0","source":{"id":"2411.15945","kind":"arxiv","version":1}},"canonical_sha256":"53acf5c441573784e046d802eaf4d075da3cbbc43338390c27462aa21d3ae6a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53acf5c441573784e046d802eaf4d075da3cbbc43338390c27462aa21d3ae6a3","first_computed_at":"2026-07-05T09:39:44.154916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:44.154916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ReqxNryYsS81BZop9WxIM2W/wjMefCasThwMwUHH/LCJAejSbVPnxhy2rixxZnB7iBqcg7J1GlKe2Cu5Xw3DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:44.155404Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dffdf56124ce9e76a44b2191ed14a515e8fe919479de960457397cf53781de07","sha256:be4d33d152eeb7c780dfc36b970c140c4863ded93a79369e0a0c6002707823b7"],"state_sha256":"9e5e43e70fc7181eea1e4898907c3de539996da38a5742401d0bd726eabf39b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHfEv4NgQ6B1rK6DEcoN6YAlx0WkO74Ls1yf5QEHvmnHCACLmdRgLUdQkVjnHmVAM+zzW3ykMvAo6TMWCsxTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:39:57.864734Z","bundle_sha256":"5f7f088c1bd3f8da3c916717db43548a1ef06927498c44be7fcf868bc9818a6e"}}