{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VWCKQYWYMFQJL2KBSPLQPOYMXT","short_pith_number":"pith:VWCKQYWY","canonical_record":{"source":{"id":"1710.05270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-15T03:38:32Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d2fe80ae75939931b12ffb0fb76a08b8fa92c76624e6de7e5e2da899dca13489","abstract_canon_sha256":"fe9053a4a49aff45e8c6babad9f6543b37f6606e40988a2a34ac7a41ea17d76d"},"schema_version":"1.0"},"canonical_sha256":"ad84a862d8616095e94193d707bb0cbcd0688715d5cd3673dd17b5eead86ca14","source":{"kind":"arxiv","id":"1710.05270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05270","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05270v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05270","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"VWCKQYWYMFQJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VWCKQYWYMFQJL2KB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VWCKQYWY","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VWCKQYWYMFQJL2KBSPLQPOYMXT","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-15T03:38:32Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d2fe80ae75939931b12ffb0fb76a08b8fa92c76624e6de7e5e2da899dca13489","abstract_canon_sha256":"fe9053a4a49aff45e8c6babad9f6543b37f6606e40988a2a34ac7a41ea17d76d"},"schema_version":"1.0"},"canonical_sha256":"ad84a862d8616095e94193d707bb0cbcd0688715d5cd3673dd17b5eead86ca14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:53.795896Z","signature_b64":"Y/U0zlT9xhAtAhY79Y9Qrh3tuC0fIdSLcATBgdVQQHPhVETpONeMyf4HqgkgnAdpn2yovIFjpLmNqv/JkvhpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad84a862d8616095e94193d707bb0cbcd0688715d5cd3673dd17b5eead86ca14","last_reissued_at":"2026-05-18T00:32:53.795214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:53.795214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05270","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":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FrodZGjCZtYA36BMbBpdk2UaUH3cDjCHzP29F+q+vAfFVJEUuxkH91Wec9MQdiRJhSAPCYVayzaeFTW44yT9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:20:00.436023Z"},"content_sha256":"5a6f14516674e0c0606fd8babac576135afa1d9a9ed961665f9bb9e027dec6a9","schema_version":"1.0","event_id":"sha256:5a6f14516674e0c0606fd8babac576135afa1d9a9ed961665f9bb9e027dec6a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VWCKQYWYMFQJL2KBSPLQPOYMXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Infinite RBMs with Frank-Wolfe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexander Ihler, Qiang Liu, Wei Ping","submitted_at":"2017-10-15T03:38:32Z","abstract_excerpt":"In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05270","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":""},"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":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ax/oriMiaeUNi9/kG8oiIfYEBZMbSSrZtW+7r4yqZdehHRxPk3jqMa7WS59m+sn1S74XW0/HLFBAnq4Jlu7YBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:20:00.436807Z"},"content_sha256":"6d10ce65070dc12d68e9a72f3569455b07e999f1daa8b92c8e9454156dbc3813","schema_version":"1.0","event_id":"sha256:6d10ce65070dc12d68e9a72f3569455b07e999f1daa8b92c8e9454156dbc3813"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/bundle.json","state_url":"https://pith.science/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/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":"2026-05-31T17:20:00Z","links":{"resolver":"https://pith.science/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT","bundle":"https://pith.science/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/bundle.json","state":"https://pith.science/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWCKQYWYMFQJL2KBSPLQPOYMXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VWCKQYWYMFQJL2KBSPLQPOYMXT","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":"fe9053a4a49aff45e8c6babad9f6543b37f6606e40988a2a34ac7a41ea17d76d","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-15T03:38:32Z","title_canon_sha256":"d2fe80ae75939931b12ffb0fb76a08b8fa92c76624e6de7e5e2da899dca13489"},"schema_version":"1.0","source":{"id":"1710.05270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05270","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05270v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05270","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"VWCKQYWYMFQJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VWCKQYWYMFQJL2KB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VWCKQYWY","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:6d10ce65070dc12d68e9a72f3569455b07e999f1daa8b92c8e9454156dbc3813","target":"graph","created_at":"2026-05-18T00:32:53Z","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":"In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be u","authors_text":"Alexander Ihler, Qiang Liu, Wei Ping","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-15T03:38:32Z","title":"Learning Infinite RBMs with Frank-Wolfe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05270","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":"sha256:5a6f14516674e0c0606fd8babac576135afa1d9a9ed961665f9bb9e027dec6a9","target":"record","created_at":"2026-05-18T00:32:53Z","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":"fe9053a4a49aff45e8c6babad9f6543b37f6606e40988a2a34ac7a41ea17d76d","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-15T03:38:32Z","title_canon_sha256":"d2fe80ae75939931b12ffb0fb76a08b8fa92c76624e6de7e5e2da899dca13489"},"schema_version":"1.0","source":{"id":"1710.05270","kind":"arxiv","version":1}},"canonical_sha256":"ad84a862d8616095e94193d707bb0cbcd0688715d5cd3673dd17b5eead86ca14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad84a862d8616095e94193d707bb0cbcd0688715d5cd3673dd17b5eead86ca14","first_computed_at":"2026-05-18T00:32:53.795214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:53.795214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/U0zlT9xhAtAhY79Y9Qrh3tuC0fIdSLcATBgdVQQHPhVETpONeMyf4HqgkgnAdpn2yovIFjpLmNqv/JkvhpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:53.795896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a6f14516674e0c0606fd8babac576135afa1d9a9ed961665f9bb9e027dec6a9","sha256:6d10ce65070dc12d68e9a72f3569455b07e999f1daa8b92c8e9454156dbc3813"],"state_sha256":"a3bacc3a7651e0485983f76bb97906953a9cbd88420a36a02ad640c5198bc98d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j1MgBtjSkYbDEddjvITS8qmb5nNtlT1XI9lMnoeg1R4tsm0GblVTxRCnn+iNV5nRBUncmvtd4s5+uG5c5E5qCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:20:00.440871Z","bundle_sha256":"1cd1d3c473c2e6832a135cb0cf6b21fa25f9c650d52591bfe87d54dfa94f1819"}}