{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5MARD7ZWG2R2XH3QIXS2FS2RLA","short_pith_number":"pith:5MARD7ZW","schema_version":"1.0","canonical_sha256":"eb0111ff3636a3ab9f7045e5a2cb51580f7c03166b02f78076db5dc72cde4a55","source":{"kind":"arxiv","id":"1905.10452","version":1},"attestation_state":"computed","paper":{"title":"Additive Noise Annealing and Approximation Properties of Quantized Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Gian Paolo Leonardi, Luca Benini, Lukas Cavigelli, Marko Bertogna, Matteo Spallanzani","submitted_at":"2019-05-24T21:30:54Z","abstract_excerpt":"We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in particular that any Lipschitz-continuous map defined on a hypercube can be uniformly approximated by a quantized neural network. We then focus on the regularization effect of additive noise on the arguments of multi-step functions inherent to the quantization of continuous variables. In particular, when the expectation operator is applied to a non-differentia"},"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":"1905.10452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-24T21:30:54Z","cross_cats_sorted":["cs.CV","stat.ML"],"title_canon_sha256":"44d7a052c062c9146384720865f20193ea0b678f6d3a3668fd62a5b4e9a8de97","abstract_canon_sha256":"6574953e69e6e9d101b349923af5d3203ccba978c6f04f5bd31b50fd95167e13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:53.601222Z","signature_b64":"CLv45a9NfNvohEJkxN0kwT+3SEjKw42hb4tn5uvxVuPeKjb5l40mtSfwe+VG0PrDP3Ck7ioBroI3/liTeL3oBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb0111ff3636a3ab9f7045e5a2cb51580f7c03166b02f78076db5dc72cde4a55","last_reissued_at":"2026-05-17T23:44:53.600723Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:53.600723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Additive Noise Annealing and Approximation Properties of Quantized Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Gian Paolo Leonardi, Luca Benini, Lukas Cavigelli, Marko Bertogna, Matteo Spallanzani","submitted_at":"2019-05-24T21:30:54Z","abstract_excerpt":"We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in particular that any Lipschitz-continuous map defined on a hypercube can be uniformly approximated by a quantized neural network. We then focus on the regularization effect of additive noise on the arguments of multi-step functions inherent to the quantization of continuous variables. In particular, when the expectation operator is applied to a non-differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10452","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.10452","created_at":"2026-05-17T23:44:53.600813+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.10452v1","created_at":"2026-05-17T23:44:53.600813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10452","created_at":"2026-05-17T23:44:53.600813+00:00"},{"alias_kind":"pith_short_12","alias_value":"5MARD7ZWG2R2","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5MARD7ZWG2R2XH3Q","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5MARD7ZW","created_at":"2026-05-18T12:33:10.108867+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/5MARD7ZWG2R2XH3QIXS2FS2RLA","json":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA.json","graph_json":"https://pith.science/api/pith-number/5MARD7ZWG2R2XH3QIXS2FS2RLA/graph.json","events_json":"https://pith.science/api/pith-number/5MARD7ZWG2R2XH3QIXS2FS2RLA/events.json","paper":"https://pith.science/paper/5MARD7ZW"},"agent_actions":{"view_html":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA","download_json":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA.json","view_paper":"https://pith.science/paper/5MARD7ZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.10452&json=true","fetch_graph":"https://pith.science/api/pith-number/5MARD7ZWG2R2XH3QIXS2FS2RLA/graph.json","fetch_events":"https://pith.science/api/pith-number/5MARD7ZWG2R2XH3QIXS2FS2RLA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA/action/storage_attestation","attest_author":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA/action/author_attestation","sign_citation":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA/action/citation_signature","submit_replication":"https://pith.science/pith/5MARD7ZWG2R2XH3QIXS2FS2RLA/action/replication_record"}},"created_at":"2026-05-17T23:44:53.600813+00:00","updated_at":"2026-05-17T23:44:53.600813+00:00"}