{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3USR2YVSBC7YLVQIY4KGRERR7V","short_pith_number":"pith:3USR2YVS","canonical_record":{"source":{"id":"1510.03009","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-11T04:32:39Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"2c373e18c2bbd10e0d4aa20cf839b62ed10313eb44882a62eec42cfdee0e7cca","abstract_canon_sha256":"9e9f3ad253963ca902e8a4b89514b3383d0beaf8e6da5a1fecefcb1839c50b43"},"schema_version":"1.0"},"canonical_sha256":"dd251d62b208bf85d608c714689231fd7ce568c5c2d42a776006885fa31530e1","source":{"kind":"arxiv","id":"1510.03009","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03009","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03009v3","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03009","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"3USR2YVSBC7Y","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3USR2YVSBC7YLVQI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3USR2YVS","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3USR2YVSBC7YLVQIY4KGRERR7V","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03009","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-11T04:32:39Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"2c373e18c2bbd10e0d4aa20cf839b62ed10313eb44882a62eec42cfdee0e7cca","abstract_canon_sha256":"9e9f3ad253963ca902e8a4b89514b3383d0beaf8e6da5a1fecefcb1839c50b43"},"schema_version":"1.0"},"canonical_sha256":"dd251d62b208bf85d608c714689231fd7ce568c5c2d42a776006885fa31530e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:57.194733Z","signature_b64":"A7G55Ze1hrkGchvoQBqzA0/NGrnGmXNP4TsgS0AZxf4EtVVETZtyBcEAg2mJX4UH1h13lZwAVv32wn1LHFT/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd251d62b208bf85d608c714689231fd7ce568c5c2d42a776006885fa31530e1","last_reissued_at":"2026-05-18T01:19:57.193886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:57.193886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03009","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGf/LQ9Mc9ePXPw0sYljSJP8Dqbg9PxnhxgAsOhK9OSuhiYNe2S+HzaFu4HRKzrWrfXbTYGEapRaDjC/Nn0EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:01:58.324390Z"},"content_sha256":"f758e5ec81d9905780b8929ac1697c7c8bb1d33496e5579f6dbb482490b5e3e4","schema_version":"1.0","event_id":"sha256:f758e5ec81d9905780b8929ac1697c7c8bb1d33496e5579f6dbb482490b5e3e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3USR2YVSBC7YLVQIY4KGRERR7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neural Networks with Few Multiplications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE"],"primary_cat":"cs.LG","authors_text":"Matthieu Courbariaux, Roland Memisevic, Yoshua Bengio, Zhouhan Lin","submitted_at":"2015-10-11T04:32:39Z","abstract_excerpt":"For most deep learning algorithms training is notoriously time consuming. Since most of the computation in training neural networks is typically spent on floating point multiplications, we investigate an approach to training that eliminates the need for most of these. Our method consists of two parts: First we stochastically binarize weights to convert multiplications involved in computing hidden states to sign changes. Second, while back-propagating error derivatives, in addition to binarizing the weights, we quantize the representations at each layer to convert the remaining multiplications "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03009","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUM2uVr9phV6w1yFqClGZ3n5WdroBob1WeSgMBJxPHTG9TIpZrn8vdLQ5E5XmuNMyaY88QR3te2/7Vfwcv/QCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:01:58.325068Z"},"content_sha256":"eab540494ca3e3b73cd1fc2f227f4f137ee21efafa70e7f80c7bc281369d53a0","schema_version":"1.0","event_id":"sha256:eab540494ca3e3b73cd1fc2f227f4f137ee21efafa70e7f80c7bc281369d53a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3USR2YVSBC7YLVQIY4KGRERR7V/bundle.json","state_url":"https://pith.science/pith/3USR2YVSBC7YLVQIY4KGRERR7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3USR2YVSBC7YLVQIY4KGRERR7V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T01:01:58Z","links":{"resolver":"https://pith.science/pith/3USR2YVSBC7YLVQIY4KGRERR7V","bundle":"https://pith.science/pith/3USR2YVSBC7YLVQIY4KGRERR7V/bundle.json","state":"https://pith.science/pith/3USR2YVSBC7YLVQIY4KGRERR7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3USR2YVSBC7YLVQIY4KGRERR7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3USR2YVSBC7YLVQIY4KGRERR7V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9e9f3ad253963ca902e8a4b89514b3383d0beaf8e6da5a1fecefcb1839c50b43","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-11T04:32:39Z","title_canon_sha256":"2c373e18c2bbd10e0d4aa20cf839b62ed10313eb44882a62eec42cfdee0e7cca"},"schema_version":"1.0","source":{"id":"1510.03009","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03009","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03009v3","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03009","created_at":"2026-05-18T01:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"3USR2YVSBC7Y","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3USR2YVSBC7YLVQI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3USR2YVS","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:eab540494ca3e3b73cd1fc2f227f4f137ee21efafa70e7f80c7bc281369d53a0","target":"graph","created_at":"2026-05-18T01:19:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For most deep learning algorithms training is notoriously time consuming. Since most of the computation in training neural networks is typically spent on floating point multiplications, we investigate an approach to training that eliminates the need for most of these. Our method consists of two parts: First we stochastically binarize weights to convert multiplications involved in computing hidden states to sign changes. Second, while back-propagating error derivatives, in addition to binarizing the weights, we quantize the representations at each layer to convert the remaining multiplications ","authors_text":"Matthieu Courbariaux, Roland Memisevic, Yoshua Bengio, Zhouhan Lin","cross_cats":["cs.NE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-11T04:32:39Z","title":"Neural Networks with Few Multiplications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03009","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f758e5ec81d9905780b8929ac1697c7c8bb1d33496e5579f6dbb482490b5e3e4","target":"record","created_at":"2026-05-18T01:19:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9e9f3ad253963ca902e8a4b89514b3383d0beaf8e6da5a1fecefcb1839c50b43","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-10-11T04:32:39Z","title_canon_sha256":"2c373e18c2bbd10e0d4aa20cf839b62ed10313eb44882a62eec42cfdee0e7cca"},"schema_version":"1.0","source":{"id":"1510.03009","kind":"arxiv","version":3}},"canonical_sha256":"dd251d62b208bf85d608c714689231fd7ce568c5c2d42a776006885fa31530e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd251d62b208bf85d608c714689231fd7ce568c5c2d42a776006885fa31530e1","first_computed_at":"2026-05-18T01:19:57.193886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:57.193886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A7G55Ze1hrkGchvoQBqzA0/NGrnGmXNP4TsgS0AZxf4EtVVETZtyBcEAg2mJX4UH1h13lZwAVv32wn1LHFT/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:57.194733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03009","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f758e5ec81d9905780b8929ac1697c7c8bb1d33496e5579f6dbb482490b5e3e4","sha256:eab540494ca3e3b73cd1fc2f227f4f137ee21efafa70e7f80c7bc281369d53a0"],"state_sha256":"63ef3b0b75ff0992850f0be00a5ce608c853c0d777cdf6bb9c1f850a0df8b9ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BTEJF1XpXY3hG5OXYNYiw3LfFOhyGN3FG2bZTAD66z9OdxGRxffg5Pwo4T3h/D9mMDbWjr9anEvOc3fAKUIRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:01:58.328923Z","bundle_sha256":"b23e84d4a7e4192bdc41355bf4b461761f8314e86b91a4478e30f918e8e34be3"}}