{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V7AETLVR77MUZIHVDQN354LV4O","short_pith_number":"pith:V7AETLVR","schema_version":"1.0","canonical_sha256":"afc049aeb1ffd94ca0f51c1bbef175e385509e48456f77bd77def602831ee188","source":{"kind":"arxiv","id":"1702.00458","version":5},"attestation_state":"computed","paper":{"title":"Convergence Results for Neural Networks via Electrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","physics.data-an"],"primary_cat":"cs.DS","authors_text":"Qiuyi Zhang, Rina Panigrahy, Sushant Sachdeva","submitted_at":"2017-02-01T21:25:13Z","abstract_excerpt":"We study whether a depth two neural network can learn another depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following question in electrodynamics: Given $k$ fixed protons in $\\mathbb{R}^d,$ and $k$ electrons, each moving due to the attractive force from the protons and repulsive force from the remaining electrons, whether at equilibrium all the electrons will be matched up with the protons, up to a permutation. Under the standard electrical force, this follows "},"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":"1702.00458","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-01T21:25:13Z","cross_cats_sorted":["cs.LG","physics.data-an"],"title_canon_sha256":"b1d60d007882d441df2be3949bdc2467ce560aa7d2cf6655231dc503af97d0f8","abstract_canon_sha256":"0adca145dcda326cb91b5d2d1d93ddf55d0f6708ed9274b43251c61d780441bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:03.815755Z","signature_b64":"s7BTs2+dsbuYdVvbH8ZYQaGNVwmVM9KGT3uoMAm+meYlhMxA+TmfylaBMrwO94IkfJsn+mPCuEiOmDfRIQ6ZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc049aeb1ffd94ca0f51c1bbef175e385509e48456f77bd77def602831ee188","last_reissued_at":"2026-05-17T23:59:03.815156Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:03.815156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Results for Neural Networks via Electrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","physics.data-an"],"primary_cat":"cs.DS","authors_text":"Qiuyi Zhang, Rina Panigrahy, Sushant Sachdeva","submitted_at":"2017-02-01T21:25:13Z","abstract_excerpt":"We study whether a depth two neural network can learn another depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following question in electrodynamics: Given $k$ fixed protons in $\\mathbb{R}^d,$ and $k$ electrons, each moving due to the attractive force from the protons and repulsive force from the remaining electrons, whether at equilibrium all the electrons will be matched up with the protons, up to a permutation. Under the standard electrical force, this follows "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00458","kind":"arxiv","version":5},"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":"1702.00458","created_at":"2026-05-17T23:59:03.815233+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00458v5","created_at":"2026-05-17T23:59:03.815233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00458","created_at":"2026-05-17T23:59:03.815233+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7AETLVR77MU","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7AETLVR77MUZIHV","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7AETLVR","created_at":"2026-05-18T12:31:49.984773+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/V7AETLVR77MUZIHVDQN354LV4O","json":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O.json","graph_json":"https://pith.science/api/pith-number/V7AETLVR77MUZIHVDQN354LV4O/graph.json","events_json":"https://pith.science/api/pith-number/V7AETLVR77MUZIHVDQN354LV4O/events.json","paper":"https://pith.science/paper/V7AETLVR"},"agent_actions":{"view_html":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O","download_json":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O.json","view_paper":"https://pith.science/paper/V7AETLVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00458&json=true","fetch_graph":"https://pith.science/api/pith-number/V7AETLVR77MUZIHVDQN354LV4O/graph.json","fetch_events":"https://pith.science/api/pith-number/V7AETLVR77MUZIHVDQN354LV4O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O/action/storage_attestation","attest_author":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O/action/author_attestation","sign_citation":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O/action/citation_signature","submit_replication":"https://pith.science/pith/V7AETLVR77MUZIHVDQN354LV4O/action/replication_record"}},"created_at":"2026-05-17T23:59:03.815233+00:00","updated_at":"2026-05-17T23:59:03.815233+00:00"}