{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:IE2NRFG2IJGMNDGALDESQL6SIX","short_pith_number":"pith:IE2NRFG2","schema_version":"1.0","canonical_sha256":"4134d894da424cc68cc058c9282fd245eea1168e7cd0a79fba3628c2c46438ea","source":{"kind":"arxiv","id":"1910.11923","version":2},"attestation_state":"computed","paper":{"title":"Learning Boolean Circuits with Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Eran Malach, Shai Shalev-Shwartz","submitted_at":"2019-10-25T20:26:13Z","abstract_excerpt":"While on some natural distributions, neural-networks are trained efficiently using gradient-based algorithms, it is known that learning them is computationally hard in the worst-case. To separate hard from easy to learn distributions, we observe the property of local correlation: correlation between local patterns of the input and the target label. We focus on learning deep neural-networks using a gradient-based algorithm, when the target function is a tree-structured Boolean circuit. We show that in this case, the existence of correlation between the gates of the circuit and the target label "},"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":"1910.11923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-25T20:26:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c96f0ed4db20bb8bc965bd1b7bbf204c7b446d6288399249915444361a72a3e6","abstract_canon_sha256":"482ab2355bb91b7939ea5b0815065193bc36853824ae6597ef3a40ec78949587"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:34:18.914730Z","signature_b64":"qYUtNyZr13HloSg8zJpQr7PQAnQVOCI9mq4y4F98bcR/oVTGbWhn63xIZHKZHgT/otCmdNtke+7+4diNyTo9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4134d894da424cc68cc058c9282fd245eea1168e7cd0a79fba3628c2c46438ea","last_reissued_at":"2026-07-05T00:34:18.914339Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:34:18.914339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Boolean Circuits with Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Eran Malach, Shai Shalev-Shwartz","submitted_at":"2019-10-25T20:26:13Z","abstract_excerpt":"While on some natural distributions, neural-networks are trained efficiently using gradient-based algorithms, it is known that learning them is computationally hard in the worst-case. To separate hard from easy to learn distributions, we observe the property of local correlation: correlation between local patterns of the input and the target label. We focus on learning deep neural-networks using a gradient-based algorithm, when the target function is a tree-structured Boolean circuit. We show that in this case, the existence of correlation between the gates of the circuit and the target label "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.11923","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.11923/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1910.11923","created_at":"2026-07-05T00:34:18.914400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.11923v2","created_at":"2026-07-05T00:34:18.914400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.11923","created_at":"2026-07-05T00:34:18.914400+00:00"},{"alias_kind":"pith_short_12","alias_value":"IE2NRFG2IJGM","created_at":"2026-07-05T00:34:18.914400+00:00"},{"alias_kind":"pith_short_16","alias_value":"IE2NRFG2IJGMNDGA","created_at":"2026-07-05T00:34:18.914400+00:00"},{"alias_kind":"pith_short_8","alias_value":"IE2NRFG2","created_at":"2026-07-05T00:34:18.914400+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/IE2NRFG2IJGMNDGALDESQL6SIX","json":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX.json","graph_json":"https://pith.science/api/pith-number/IE2NRFG2IJGMNDGALDESQL6SIX/graph.json","events_json":"https://pith.science/api/pith-number/IE2NRFG2IJGMNDGALDESQL6SIX/events.json","paper":"https://pith.science/paper/IE2NRFG2"},"agent_actions":{"view_html":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX","download_json":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX.json","view_paper":"https://pith.science/paper/IE2NRFG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.11923&json=true","fetch_graph":"https://pith.science/api/pith-number/IE2NRFG2IJGMNDGALDESQL6SIX/graph.json","fetch_events":"https://pith.science/api/pith-number/IE2NRFG2IJGMNDGALDESQL6SIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX/action/storage_attestation","attest_author":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX/action/author_attestation","sign_citation":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX/action/citation_signature","submit_replication":"https://pith.science/pith/IE2NRFG2IJGMNDGALDESQL6SIX/action/replication_record"}},"created_at":"2026-07-05T00:34:18.914400+00:00","updated_at":"2026-07-05T00:34:18.914400+00:00"}