{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QUVGPUBWQKW5CHWHDN52E3NZJW","short_pith_number":"pith:QUVGPUBW","canonical_record":{"source":{"id":"1803.08577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-22T20:32:32Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"612be2e6020ecd4e5327207d1eeaa1c8c9972ddf5ca8c605f8c96630c65ffdac","abstract_canon_sha256":"226272f32df1e2351f27a1bc7b61e778489663f8b45e715d29c76ac92c94f991"},"schema_version":"1.0"},"canonical_sha256":"852a67d03682add11ec71b7ba26db94d864f70c3de897ce3815024aef9f9681f","source":{"kind":"arxiv","id":"1803.08577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08577","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08577v1","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08577","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"QUVGPUBWQKW5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QUVGPUBWQKW5CHWH","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QUVGPUBW","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QUVGPUBWQKW5CHWHDN52E3NZJW","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-22T20:32:32Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"612be2e6020ecd4e5327207d1eeaa1c8c9972ddf5ca8c605f8c96630c65ffdac","abstract_canon_sha256":"226272f32df1e2351f27a1bc7b61e778489663f8b45e715d29c76ac92c94f991"},"schema_version":"1.0"},"canonical_sha256":"852a67d03682add11ec71b7ba26db94d864f70c3de897ce3815024aef9f9681f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:19.245220Z","signature_b64":"udnR2yHVPv7Xiy4dgAGNF/006PGpFG5PDicZg+/DrlwyvbQIYjwuW/z07d/HZDxTukG/8TK/YEOSHw5GH6tjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"852a67d03682add11ec71b7ba26db94d864f70c3de897ce3815024aef9f9681f","last_reissued_at":"2026-05-18T00:20:19.244409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:19.244409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08577","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tea3u0GhRXhHHkvaWh5RF5HZULJ/E1LuKbPtuzRcSWp9Sv9UQZwQL6Ch52A5GieQVc2OrSodZEjCNdms0vGeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:44:01.039626Z"},"content_sha256":"88a4c68b8d6edbd3f31d44e7ceabd4b8bd21d1b656c05f559f381fff80dd697b","schema_version":"1.0","event_id":"sha256:88a4c68b8d6edbd3f31d44e7ceabd4b8bd21d1b656c05f559f381fff80dd697b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QUVGPUBWQKW5CHWHDN52E3NZJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unbiased scalable softmax optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Francois Fagan, Garud Iyengar","submitted_at":"2018-03-22T20:32:32Z","abstract_excerpt":"Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing literature of efficiently computable but biased estimates of the softmax. In this paper we propose the first unbiased algorithms for maximizing the softmax likelihood whose work per iteration is independent of the number of classes and datapoints (and no extra work is required at the end of each epoch). We show that our proposed unbiased methods comprehensively outp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08577","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ygO1OVvDai+uuEZi4ebeaGIYGzsEHgScs2mZfWfNPJgM0YpBnEtywD2fpUHZzOu+MzFGnFmq7BbnSoJzj6cBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T07:44:01.040101Z"},"content_sha256":"93b395b75a8f82ef85bd7b79f64f9e312dd50e5d2998a78cb207f2de646fb8a2","schema_version":"1.0","event_id":"sha256:93b395b75a8f82ef85bd7b79f64f9e312dd50e5d2998a78cb207f2de646fb8a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/bundle.json","state_url":"https://pith.science/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/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":"2026-06-06T07:44:01Z","links":{"resolver":"https://pith.science/pith/QUVGPUBWQKW5CHWHDN52E3NZJW","bundle":"https://pith.science/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/bundle.json","state":"https://pith.science/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUVGPUBWQKW5CHWHDN52E3NZJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QUVGPUBWQKW5CHWHDN52E3NZJW","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":"226272f32df1e2351f27a1bc7b61e778489663f8b45e715d29c76ac92c94f991","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-22T20:32:32Z","title_canon_sha256":"612be2e6020ecd4e5327207d1eeaa1c8c9972ddf5ca8c605f8c96630c65ffdac"},"schema_version":"1.0","source":{"id":"1803.08577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08577","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08577v1","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08577","created_at":"2026-05-18T00:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"QUVGPUBWQKW5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QUVGPUBWQKW5CHWH","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QUVGPUBW","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:93b395b75a8f82ef85bd7b79f64f9e312dd50e5d2998a78cb207f2de646fb8a2","target":"graph","created_at":"2026-05-18T00:20:19Z","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":"Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing literature of efficiently computable but biased estimates of the softmax. In this paper we propose the first unbiased algorithms for maximizing the softmax likelihood whose work per iteration is independent of the number of classes and datapoints (and no extra work is required at the end of each epoch). We show that our proposed unbiased methods comprehensively outp","authors_text":"Francois Fagan, Garud Iyengar","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-22T20:32:32Z","title":"Unbiased scalable softmax optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08577","kind":"arxiv","version":1},"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":"sha256:88a4c68b8d6edbd3f31d44e7ceabd4b8bd21d1b656c05f559f381fff80dd697b","target":"record","created_at":"2026-05-18T00:20:19Z","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":"226272f32df1e2351f27a1bc7b61e778489663f8b45e715d29c76ac92c94f991","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-22T20:32:32Z","title_canon_sha256":"612be2e6020ecd4e5327207d1eeaa1c8c9972ddf5ca8c605f8c96630c65ffdac"},"schema_version":"1.0","source":{"id":"1803.08577","kind":"arxiv","version":1}},"canonical_sha256":"852a67d03682add11ec71b7ba26db94d864f70c3de897ce3815024aef9f9681f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"852a67d03682add11ec71b7ba26db94d864f70c3de897ce3815024aef9f9681f","first_computed_at":"2026-05-18T00:20:19.244409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:19.244409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"udnR2yHVPv7Xiy4dgAGNF/006PGpFG5PDicZg+/DrlwyvbQIYjwuW/z07d/HZDxTukG/8TK/YEOSHw5GH6tjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:19.245220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88a4c68b8d6edbd3f31d44e7ceabd4b8bd21d1b656c05f559f381fff80dd697b","sha256:93b395b75a8f82ef85bd7b79f64f9e312dd50e5d2998a78cb207f2de646fb8a2"],"state_sha256":"69244decb6a8e705fb0f7d157ab2366246baaf8e20c464b759f4546c7e0b4272"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kE1xh14BQ4+P4QToLIXHK4HrQQvMWNkRssJKEAoUnGFDchdQuI5wxPa/QZUqKjy+MWpa3Q+l9hIip0vNpsgbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T07:44:01.042574Z","bundle_sha256":"0aafe8d386cfaa1b060e57d58a5cb0473cc6f2542c4392063fa3a7028621c50c"}}