{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5QXVFMCLVZX6XHTQI3Y2BP4PT7","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":"3bd4c0c2cb16b13f1c0d6dde810c7606bf011501a3558c6d95d51371dc1a76be","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-11T18:49:07Z","title_canon_sha256":"13e09c797f13ef8b12d22d5ba89ed1bf3a7072c87ef27b7ff15334bb9a813b1a"},"schema_version":"1.0","source":{"id":"1712.03942","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03942","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03942v3","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03942","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"pith_short_12","alias_value":"5QXVFMCLVZX6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5QXVFMCLVZX6XHTQ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5QXVFMCL","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:539c6d27fbe6a61cb44ddf4e9363b0c65d24b6d10b5f512b0b4688847f6d6447","target":"graph","created_at":"2026-05-18T00:13:50Z","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":"A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of matrix multiplications in DNN layers by casting matrix multiplications as 2-layer sum-product networks (SPNs) (arithmetic circuits) and learning their (ternary) edge weights from data. The SPNs disentangle multiplication and addition operations and enable us to impose a budget on the number of multiplication operations. Combining our method with knowledge di","authors_text":"Anima Anandkumar, Aran Khanna, Michael Tschannen","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-11T18:49:07Z","title":"StrassenNets: Deep Learning with a Multiplication Budget"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03942","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":"sha256:20edaa9157c7fa3018c4495f086c193b79a25a35508950158bda3ad50a7fb3d5","target":"record","created_at":"2026-05-18T00:13:50Z","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":"3bd4c0c2cb16b13f1c0d6dde810c7606bf011501a3558c6d95d51371dc1a76be","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-11T18:49:07Z","title_canon_sha256":"13e09c797f13ef8b12d22d5ba89ed1bf3a7072c87ef27b7ff15334bb9a813b1a"},"schema_version":"1.0","source":{"id":"1712.03942","kind":"arxiv","version":3}},"canonical_sha256":"ec2f52b04bae6feb9e7046f1a0bf8f9fc9bde6fd1f70b50b83efaff97fbfdef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec2f52b04bae6feb9e7046f1a0bf8f9fc9bde6fd1f70b50b83efaff97fbfdef9","first_computed_at":"2026-05-18T00:13:50.900014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:50.900014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B66pXgiycbyAZ6HRHbKnOLjRO+nBtG/hZSaY9YEM41dWcbAyrb69QIi+KEwHqF37gekci2MY5TrZ714FxzQKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:50.900681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03942","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20edaa9157c7fa3018c4495f086c193b79a25a35508950158bda3ad50a7fb3d5","sha256:539c6d27fbe6a61cb44ddf4e9363b0c65d24b6d10b5f512b0b4688847f6d6447"],"state_sha256":"8f071ecff1da8c115f7a0713631a8de5943bc9cafdf600d99669bbc9aa6ee53a"}