{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VTPKUNURIPLLNJIUCK2X5UDLYY","short_pith_number":"pith:VTPKUNUR","canonical_record":{"source":{"id":"1911.07971","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T21:48:01Z","cross_cats_sorted":["cs.DC","cs.IT","math.IT","stat.ML"],"title_canon_sha256":"bdc78650cda94fcf1f2ff621bced78d1b3b9091c0ccd9927f0238eac3ab0ea7d","abstract_canon_sha256":"d455f5d431ffb76868b8c198b2fe9195a5d28057d4028da23d50162fd128dd33"},"schema_version":"1.0"},"canonical_sha256":"acdeaa369143d6b6a51412b57ed06bc63713fa26bdfb91ab1612cbabd694c5be","source":{"kind":"arxiv","id":"1911.07971","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.07971","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1911.07971v4","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.07971","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"VTPKUNURIPLL","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_16","alias_value":"VTPKUNURIPLLNJIU","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_8","alias_value":"VTPKUNUR","created_at":"2026-07-05T02:02:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VTPKUNURIPLLNJIUCK2X5UDLYY","target":"record","payload":{"canonical_record":{"source":{"id":"1911.07971","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T21:48:01Z","cross_cats_sorted":["cs.DC","cs.IT","math.IT","stat.ML"],"title_canon_sha256":"bdc78650cda94fcf1f2ff621bced78d1b3b9091c0ccd9927f0238eac3ab0ea7d","abstract_canon_sha256":"d455f5d431ffb76868b8c198b2fe9195a5d28057d4028da23d50162fd128dd33"},"schema_version":"1.0"},"canonical_sha256":"acdeaa369143d6b6a51412b57ed06bc63713fa26bdfb91ab1612cbabd694c5be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:02:01.518293Z","signature_b64":"tVTR6lAhwSEofRLXAHatZvPyAeREYb7/DnyHiVzHFqfpPkNfu+A5GQxeRGaT56xI6iy/RP0kzhmko9SrYbupDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acdeaa369143d6b6a51412b57ed06bc63713fa26bdfb91ab1612cbabd694c5be","last_reissued_at":"2026-07-05T02:02:01.517945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:02:01.517945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.07971","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6DJ6axk4ucKUHvDqmB/+ucJuLKHzV8UIuOiAYVU/SBd6w/lo33Duu9XaqJlgRvbjbsdqahg7K9dISE3x4C5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:12:27.519683Z"},"content_sha256":"91ce469254692d423fe23db3118e9ca8beb568d45345c32ecd8e7bceaecf59f7","schema_version":"1.0","event_id":"sha256:91ce469254692d423fe23db3118e9ca8beb568d45345c32ecd8e7bceaecf59f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VTPKUNURIPLLNJIUCK2X5UDLYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"vqSGD: Vector Quantized Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Arya Mazumdar, Daniel Kane, Raj Kumar Maity, Venkata Gandikota","submitted_at":"2019-11-18T21:48:01Z","abstract_excerpt":"In this work, we present a family of vector quantization schemes \\emph{vqSGD} (Vector-Quantized Stochastic Gradient Descent) that provide an asymptotic reduction in the communication cost with convergence guarantees in first-order distributed optimization. In the process we derive the following fundamental information theoretic fact: $\\Theta(\\frac{d}{R^2})$ bits are necessary and sufficient to describe an unbiased estimator ${\\hat{g}}({g})$ for any ${g}$ in the $d$-dimensional unit sphere, under the constraint that $\\|{\\hat{g}}({g})\\|_2\\le R$ almost surely. In particular, we consider a randomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07971","kind":"arxiv","version":4},"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/1911.07971/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lg+80oLXBjWlKSX1o2XeIv1X3vuR9+FVtsj40CYQdeWQ4cH239wjWo+7Oyot/xMDuZUGzXxVV+qKbfRGOs+vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:12:27.520197Z"},"content_sha256":"e182809e232a5f6603b8d3ce1d5328606844efb472de42a2e8b3c48f03a1433a","schema_version":"1.0","event_id":"sha256:e182809e232a5f6603b8d3ce1d5328606844efb472de42a2e8b3c48f03a1433a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/bundle.json","state_url":"https://pith.science/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/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":"2026-08-05T13:12:27Z","links":{"resolver":"https://pith.science/pith/VTPKUNURIPLLNJIUCK2X5UDLYY","bundle":"https://pith.science/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/bundle.json","state":"https://pith.science/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTPKUNURIPLLNJIUCK2X5UDLYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VTPKUNURIPLLNJIUCK2X5UDLYY","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":"d455f5d431ffb76868b8c198b2fe9195a5d28057d4028da23d50162fd128dd33","cross_cats_sorted":["cs.DC","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T21:48:01Z","title_canon_sha256":"bdc78650cda94fcf1f2ff621bced78d1b3b9091c0ccd9927f0238eac3ab0ea7d"},"schema_version":"1.0","source":{"id":"1911.07971","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.07971","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1911.07971v4","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.07971","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"VTPKUNURIPLL","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_16","alias_value":"VTPKUNURIPLLNJIU","created_at":"2026-07-05T02:02:01Z"},{"alias_kind":"pith_short_8","alias_value":"VTPKUNUR","created_at":"2026-07-05T02:02:01Z"}],"graph_snapshots":[{"event_id":"sha256:e182809e232a5f6603b8d3ce1d5328606844efb472de42a2e8b3c48f03a1433a","target":"graph","created_at":"2026-07-05T02:02:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.07971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we present a family of vector quantization schemes \\emph{vqSGD} (Vector-Quantized Stochastic Gradient Descent) that provide an asymptotic reduction in the communication cost with convergence guarantees in first-order distributed optimization. In the process we derive the following fundamental information theoretic fact: $\\Theta(\\frac{d}{R^2})$ bits are necessary and sufficient to describe an unbiased estimator ${\\hat{g}}({g})$ for any ${g}$ in the $d$-dimensional unit sphere, under the constraint that $\\|{\\hat{g}}({g})\\|_2\\le R$ almost surely. In particular, we consider a randomi","authors_text":"Arya Mazumdar, Daniel Kane, Raj Kumar Maity, Venkata Gandikota","cross_cats":["cs.DC","cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T21:48:01Z","title":"vqSGD: Vector Quantized Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07971","kind":"arxiv","version":4},"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":"sha256:91ce469254692d423fe23db3118e9ca8beb568d45345c32ecd8e7bceaecf59f7","target":"record","created_at":"2026-07-05T02:02:01Z","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":"d455f5d431ffb76868b8c198b2fe9195a5d28057d4028da23d50162fd128dd33","cross_cats_sorted":["cs.DC","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T21:48:01Z","title_canon_sha256":"bdc78650cda94fcf1f2ff621bced78d1b3b9091c0ccd9927f0238eac3ab0ea7d"},"schema_version":"1.0","source":{"id":"1911.07971","kind":"arxiv","version":4}},"canonical_sha256":"acdeaa369143d6b6a51412b57ed06bc63713fa26bdfb91ab1612cbabd694c5be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acdeaa369143d6b6a51412b57ed06bc63713fa26bdfb91ab1612cbabd694c5be","first_computed_at":"2026-07-05T02:02:01.517945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:02:01.517945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVTR6lAhwSEofRLXAHatZvPyAeREYb7/DnyHiVzHFqfpPkNfu+A5GQxeRGaT56xI6iy/RP0kzhmko9SrYbupDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:02:01.518293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.07971","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91ce469254692d423fe23db3118e9ca8beb568d45345c32ecd8e7bceaecf59f7","sha256:e182809e232a5f6603b8d3ce1d5328606844efb472de42a2e8b3c48f03a1433a"],"state_sha256":"9a8044bd7f04af8af68e4daff35716673e146aff622fd4dfa4c32012945a69b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lirk8L8bSadaqMs7+LhUDPcltiab/3lLWXIuopgpAN8vS9jSkwE+FpXTQUvthkPcCPCbcPn/55nHza5w8cPzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T13:12:27.532664Z","bundle_sha256":"6ba724d44f5cec57d6dce7ddfae22d880a2650b033ee47c58bf5f8c3d7306e86"}}