{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WXILIXESU6NUFUW4FZ4C2XKUBT","short_pith_number":"pith:WXILIXES","schema_version":"1.0","canonical_sha256":"b5d0b45c92a79b42d2dc2e782d5d540cf96f21a9ddf88d5382636ac6fdd4fcb1","source":{"kind":"arxiv","id":"1708.01422","version":3},"attestation_state":"computed","paper":{"title":"Exploring the Function Space of Deep-Learning Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cond-mat.dis-nn","authors_text":"Bo Li, David Saad","submitted_at":"2017-08-04T08:38:20Z","abstract_excerpt":"The function space of deep-learning machines is investigated by studying growth in the entropy of functions of a given error with respect to a reference function, realized by a deep-learning machine. Using physics-inspired methods we study both sparsely and densely-connected architectures to discover a layer-wise convergence of candidate functions, marked by a corresponding reduction in entropy when approaching the reference function, gain insight into the importance of having a large number of layers, and observe phase transitions as the error increases."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.01422","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2017-08-04T08:38:20Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"d722ca6650fa68e0f65f438bbc4762ea4da4e5b1ae75e9119018aa2c8457da48","abstract_canon_sha256":"d5baab5ee2056e88942873159d4aca13b41332c9bb5c921269a43bbdbee8ccf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:31.452212Z","signature_b64":"98riLtSJJG9LGhROzQa+mTCpiVUlWPdlplRS68Wie4CdqkQUWLUEt2D92GG3MBgOWA0FANAdsSRd0ApzTkPpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5d0b45c92a79b42d2dc2e782d5d540cf96f21a9ddf88d5382636ac6fdd4fcb1","last_reissued_at":"2026-05-18T00:08:31.451591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:31.451591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exploring the Function Space of Deep-Learning Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cond-mat.dis-nn","authors_text":"Bo Li, David Saad","submitted_at":"2017-08-04T08:38:20Z","abstract_excerpt":"The function space of deep-learning machines is investigated by studying growth in the entropy of functions of a given error with respect to a reference function, realized by a deep-learning machine. Using physics-inspired methods we study both sparsely and densely-connected architectures to discover a layer-wise convergence of candidate functions, marked by a corresponding reduction in entropy when approaching the reference function, gain insight into the importance of having a large number of layers, and observe phase transitions as the error increases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01422","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.01422","created_at":"2026-05-18T00:08:31.451681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.01422v3","created_at":"2026-05-18T00:08:31.451681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01422","created_at":"2026-05-18T00:08:31.451681+00:00"},{"alias_kind":"pith_short_12","alias_value":"WXILIXESU6NU","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WXILIXESU6NUFUW4","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WXILIXES","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT","json":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT.json","graph_json":"https://pith.science/api/pith-number/WXILIXESU6NUFUW4FZ4C2XKUBT/graph.json","events_json":"https://pith.science/api/pith-number/WXILIXESU6NUFUW4FZ4C2XKUBT/events.json","paper":"https://pith.science/paper/WXILIXES"},"agent_actions":{"view_html":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT","download_json":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT.json","view_paper":"https://pith.science/paper/WXILIXES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.01422&json=true","fetch_graph":"https://pith.science/api/pith-number/WXILIXESU6NUFUW4FZ4C2XKUBT/graph.json","fetch_events":"https://pith.science/api/pith-number/WXILIXESU6NUFUW4FZ4C2XKUBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT/action/storage_attestation","attest_author":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT/action/author_attestation","sign_citation":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT/action/citation_signature","submit_replication":"https://pith.science/pith/WXILIXESU6NUFUW4FZ4C2XKUBT/action/replication_record"}},"created_at":"2026-05-18T00:08:31.451681+00:00","updated_at":"2026-05-18T00:08:31.451681+00:00"}