{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KMOMBBKF7YLBUX3BGZXGJISLSO","short_pith_number":"pith:KMOMBBKF","schema_version":"1.0","canonical_sha256":"531cc08545fe161a5f61366e64a24b93a910c5326c04711a2aef5b68d7782935","source":{"kind":"arxiv","id":"1909.13144","version":2},"attestation_state":"computed","paper":{"title":"Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Wei Wang, Xin Dong, Yuhang Li","submitted_at":"2019-09-28T20:14:11Z","abstract_excerpt":"We propose Additive Powers-of-Two~(APoT) quantization, an efficient non-uniform quantization scheme for the bell-shaped and long-tailed distribution of weights and activations in neural networks. By constraining all quantization levels as the sum of Powers-of-Two terms, APoT quantization enjoys high computational efficiency and a good match with the distribution of weights. A simple reparameterization of the clipping function is applied to generate a better-defined gradient for learning the clipping threshold. Moreover, weight normalization is presented to refine the distribution of weights to"},"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":"1909.13144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-09-28T20:14:11Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3a7c6d69065962cf5bf145759bf39fcefa1354ba1f8ed80a83ba80260f462086","abstract_canon_sha256":"80b0d1e366f38417fdbac407c88276256a3eccd47869c30ca8152360937dfc61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:37:47.981289Z","signature_b64":"Q1d9OdBq/QRk6PNSn0J67512tDZmDdjB1/4h34IfOQwfZxr3Rpc8ODCYwmz377kiX9YBjE1BwTKeo/nlOpdsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"531cc08545fe161a5f61366e64a24b93a910c5326c04711a2aef5b68d7782935","last_reissued_at":"2026-07-05T00:37:47.980826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:37:47.980826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Wei Wang, Xin Dong, Yuhang Li","submitted_at":"2019-09-28T20:14:11Z","abstract_excerpt":"We propose Additive Powers-of-Two~(APoT) quantization, an efficient non-uniform quantization scheme for the bell-shaped and long-tailed distribution of weights and activations in neural networks. By constraining all quantization levels as the sum of Powers-of-Two terms, APoT quantization enjoys high computational efficiency and a good match with the distribution of weights. A simple reparameterization of the clipping function is applied to generate a better-defined gradient for learning the clipping threshold. Moreover, weight normalization is presented to refine the distribution of weights to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13144","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/1909.13144/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":"1909.13144","created_at":"2026-07-05T00:37:47.980883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.13144v2","created_at":"2026-07-05T00:37:47.980883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13144","created_at":"2026-07-05T00:37:47.980883+00:00"},{"alias_kind":"pith_short_12","alias_value":"KMOMBBKF7YLB","created_at":"2026-07-05T00:37:47.980883+00:00"},{"alias_kind":"pith_short_16","alias_value":"KMOMBBKF7YLBUX3B","created_at":"2026-07-05T00:37:47.980883+00:00"},{"alias_kind":"pith_short_8","alias_value":"KMOMBBKF","created_at":"2026-07-05T00:37:47.980883+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25087","citing_title":"Neural Network Quantization by Learning Low-Loss Subspaces","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2503.03088","citing_title":"AHCQ-SAM: Toward Accurate and Hardware-Compatible Post-Training Segment Anything Model Quantization","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01866","citing_title":"ShiftLIF: Efficient Multi-Level Spiking Neurons with Power-of-Two Quantization","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO","json":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO.json","graph_json":"https://pith.science/api/pith-number/KMOMBBKF7YLBUX3BGZXGJISLSO/graph.json","events_json":"https://pith.science/api/pith-number/KMOMBBKF7YLBUX3BGZXGJISLSO/events.json","paper":"https://pith.science/paper/KMOMBBKF"},"agent_actions":{"view_html":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO","download_json":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO.json","view_paper":"https://pith.science/paper/KMOMBBKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.13144&json=true","fetch_graph":"https://pith.science/api/pith-number/KMOMBBKF7YLBUX3BGZXGJISLSO/graph.json","fetch_events":"https://pith.science/api/pith-number/KMOMBBKF7YLBUX3BGZXGJISLSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO/action/storage_attestation","attest_author":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO/action/author_attestation","sign_citation":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO/action/citation_signature","submit_replication":"https://pith.science/pith/KMOMBBKF7YLBUX3BGZXGJISLSO/action/replication_record"}},"created_at":"2026-07-05T00:37:47.980883+00:00","updated_at":"2026-07-05T00:37:47.980883+00:00"}