{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DUYUUEHDV4LWG36573UAQ7ZIBP","short_pith_number":"pith:DUYUUEHD","canonical_record":{"source":{"id":"1803.01960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-03-05T23:46:27Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"2c59d500d33227d94d758b2aa6f8f1b2384b5164e6d8f79024f7aab3152d8667","abstract_canon_sha256":"f65a1e3169ab2b5ea5801de9cfd1f11eadbc0ad12224a6a909f67354069e7e7b"},"schema_version":"1.0"},"canonical_sha256":"1d314a10e3af17636fddfee8087f280bce91c373eca2625f23a5960e097ea50e","source":{"kind":"arxiv","id":"1803.01960","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01960","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01960v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01960","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"DUYUUEHDV4LW","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DUYUUEHDV4LWG365","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DUYUUEHD","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DUYUUEHDV4LWG36573UAQ7ZIBP","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-03-05T23:46:27Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"2c59d500d33227d94d758b2aa6f8f1b2384b5164e6d8f79024f7aab3152d8667","abstract_canon_sha256":"f65a1e3169ab2b5ea5801de9cfd1f11eadbc0ad12224a6a909f67354069e7e7b"},"schema_version":"1.0"},"canonical_sha256":"1d314a10e3af17636fddfee8087f280bce91c373eca2625f23a5960e097ea50e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:55.347843Z","signature_b64":"NFflAXCmrl4rcthblALrF4qNeY8SkD4yryTJGCTtF34+CqPXq81v0GdVECVp2Wq8M4Ya8Ht7miaSFNG9BOmzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d314a10e3af17636fddfee8087f280bce91c373eca2625f23a5960e097ea50e","last_reissued_at":"2026-05-18T00:07:55.347161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:55.347161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01960","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":"2026-05-18T00:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zDl1jJzahnV5cYe+gGAK4rNrwEnqW0TDtJd3bfGCwT+RPBKBN/yexiQIYTnG2PMUlhyiMieQxfX4i4uqEPNCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:39:10.182443Z"},"content_sha256":"89046464e934a196fa7a4d6039e726e728a43e56ec5c9f9936cc7271c6dc8753","schema_version":"1.0","event_id":"sha256:89046464e934a196fa7a4d6039e726e728a43e56ec5c9f9936cc7271c6dc8753"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DUYUUEHDV4LWG36573UAQ7ZIBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics of Restricted Boltzmann Machines and related learning dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"cond-mat.dis-nn","authors_text":"Aur\\'elien Decelle, Cyril FURTLEHNER, Giancarlo Fissore","submitted_at":"2018-03-05T23:46:27Z","abstract_excerpt":"We investigate the thermodynamic properties of a Restricted Boltzmann Machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected by the spectral properties of its weight matrix $W$, we try to make a realistic analysis by averaging over an appropriate statistical ensemble of RBMs.\n  First, a phase diagram is derived. Otherwise similar to that of the Sherrington- Kirkpatrick (SK) model with ferromagnetic couplings, the RBM's phase diagram presents a ferromagnetic phase which may or may "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01960","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":""},"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":"2026-05-18T00:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfW8XhdNc1rS8svUiAOw6bdLH4B0YKkz3YK3eD4zLEEPiMY0dnQRDsREp17psyG2uBajCjBHCthgwm2Lne4ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:39:10.182793Z"},"content_sha256":"cc3b7bb84c6b5b056dc35fcc67b90fb442c1a33b40c76e84b355c175f9937783","schema_version":"1.0","event_id":"sha256:cc3b7bb84c6b5b056dc35fcc67b90fb442c1a33b40c76e84b355c175f9937783"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/bundle.json","state_url":"https://pith.science/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/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":"2026-06-07T10:39:10Z","links":{"resolver":"https://pith.science/pith/DUYUUEHDV4LWG36573UAQ7ZIBP","bundle":"https://pith.science/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/bundle.json","state":"https://pith.science/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUYUUEHDV4LWG36573UAQ7ZIBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DUYUUEHDV4LWG36573UAQ7ZIBP","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":"f65a1e3169ab2b5ea5801de9cfd1f11eadbc0ad12224a6a909f67354069e7e7b","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-03-05T23:46:27Z","title_canon_sha256":"2c59d500d33227d94d758b2aa6f8f1b2384b5164e6d8f79024f7aab3152d8667"},"schema_version":"1.0","source":{"id":"1803.01960","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01960","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01960v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01960","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"DUYUUEHDV4LW","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DUYUUEHDV4LWG365","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DUYUUEHD","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:cc3b7bb84c6b5b056dc35fcc67b90fb442c1a33b40c76e84b355c175f9937783","target":"graph","created_at":"2026-05-18T00:07:55Z","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"},"paper":{"abstract_excerpt":"We investigate the thermodynamic properties of a Restricted Boltzmann Machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected by the spectral properties of its weight matrix $W$, we try to make a realistic analysis by averaging over an appropriate statistical ensemble of RBMs.\n  First, a phase diagram is derived. Otherwise similar to that of the Sherrington- Kirkpatrick (SK) model with ferromagnetic couplings, the RBM's phase diagram presents a ferromagnetic phase which may or may ","authors_text":"Aur\\'elien Decelle, Cyril FURTLEHNER, Giancarlo Fissore","cross_cats":["cond-mat.stat-mech","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-03-05T23:46:27Z","title":"Thermodynamics of Restricted Boltzmann Machines and related learning dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01960","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":"sha256:89046464e934a196fa7a4d6039e726e728a43e56ec5c9f9936cc7271c6dc8753","target":"record","created_at":"2026-05-18T00:07:55Z","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":"f65a1e3169ab2b5ea5801de9cfd1f11eadbc0ad12224a6a909f67354069e7e7b","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-03-05T23:46:27Z","title_canon_sha256":"2c59d500d33227d94d758b2aa6f8f1b2384b5164e6d8f79024f7aab3152d8667"},"schema_version":"1.0","source":{"id":"1803.01960","kind":"arxiv","version":2}},"canonical_sha256":"1d314a10e3af17636fddfee8087f280bce91c373eca2625f23a5960e097ea50e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d314a10e3af17636fddfee8087f280bce91c373eca2625f23a5960e097ea50e","first_computed_at":"2026-05-18T00:07:55.347161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:55.347161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NFflAXCmrl4rcthblALrF4qNeY8SkD4yryTJGCTtF34+CqPXq81v0GdVECVp2Wq8M4Ya8Ht7miaSFNG9BOmzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:55.347843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01960","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89046464e934a196fa7a4d6039e726e728a43e56ec5c9f9936cc7271c6dc8753","sha256:cc3b7bb84c6b5b056dc35fcc67b90fb442c1a33b40c76e84b355c175f9937783"],"state_sha256":"b77284412b01ea58ebcea18b3b942d41e58911581e9d69a11104078260c622d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBQUBClooKV8xZqUOZOQ4RjR7mwQQSSZJrIBKALgAAeDZJUXzLVh4SkdXQ2LDBiJEtdlTX2I7idK4EsoBliBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:39:10.185762Z","bundle_sha256":"49af8b6d7100e2da1941ec7280ba9675bd87751acfb921cd29bc40c14a917886"}}