{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DQFOLOCU3KS62323GEF6DQZHDI","short_pith_number":"pith:DQFOLOCU","canonical_record":{"source":{"id":"2403.01322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-02T21:54:36Z","cross_cats_sorted":[],"title_canon_sha256":"81c58d7a0538788ed1c0a2329cd79218fd4f1c0bfc24116af5426fc1665cf9d0","abstract_canon_sha256":"cce34dbe4411dc6bce8c436b096adcc5dbdcafd4c68a03b0448df7cdda84180b"},"schema_version":"1.0"},"canonical_sha256":"1c0ae5b854daa5ed6f5b310be1c3271a2ae8973441b4d689e76113d68ac49204","source":{"kind":"arxiv","id":"2403.01322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.01322","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"2403.01322v1","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.01322","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"DQFOLOCU3KS6","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"DQFOLOCU3KS62323","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"DQFOLOCU","created_at":"2026-07-05T07:51:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DQFOLOCU3KS62323GEF6DQZHDI","target":"record","payload":{"canonical_record":{"source":{"id":"2403.01322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-02T21:54:36Z","cross_cats_sorted":[],"title_canon_sha256":"81c58d7a0538788ed1c0a2329cd79218fd4f1c0bfc24116af5426fc1665cf9d0","abstract_canon_sha256":"cce34dbe4411dc6bce8c436b096adcc5dbdcafd4c68a03b0448df7cdda84180b"},"schema_version":"1.0"},"canonical_sha256":"1c0ae5b854daa5ed6f5b310be1c3271a2ae8973441b4d689e76113d68ac49204","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:51:45.311307Z","signature_b64":"CNNa3mai1wwP5B7wMJ/d9fBzXm9FFuOJuavgJaJa/8ZdST8ycprktrc/SQklEoAm6G9LmVA4/UQzsf8jPH8RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c0ae5b854daa5ed6f5b310be1c3271a2ae8973441b4d689e76113d68ac49204","last_reissued_at":"2026-07-05T07:51:45.310827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:51:45.310827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.01322","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":"2026-07-05T07:51:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpI7nV6UbPisMBmGRgSVuAl836HUgKdaD6aQPVcD0OWSDCVLvPkQgmBP3gyCOm0H2sRRQdI43xJfN09s1Y7GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:43:40.610097Z"},"content_sha256":"5a3c511e34b972181ead62ee1b809708ea6bb3d82f1dcd764d3efd92b5035607","schema_version":"1.0","event_id":"sha256:5a3c511e34b972181ead62ee1b809708ea6bb3d82f1dcd764d3efd92b5035607"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DQFOLOCU3KS62323GEF6DQZHDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antai Xie, Ming Cao, Xiaofan Wang, Xiaoqiang Ren, Xinlei Yi","submitted_at":"2024-03-02T21:54:36Z","abstract_excerpt":"This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent (SGD) algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate $\\mathcal{O}(1/\\sqrt{nT})$ for smooth nonconvex functions, where $T$ and $n$ are the number of iterations and agents, respectively. If the global cost function additi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.01322","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.01322/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":"2026-07-05T07:51:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXDloT9cSOOjaKF8YZF+a1JHls6mR5L9aQ0tVwtxSi+Se8MCTjMBtQHHB3e1SMoKsIV/Ws+hc/WqpNABb+t/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:43:40.610587Z"},"content_sha256":"6b70edd050e8c98a7681c2503835ee9b67c1b8495b7024e4efa3c36cec09c9a5","schema_version":"1.0","event_id":"sha256:6b70edd050e8c98a7681c2503835ee9b67c1b8495b7024e4efa3c36cec09c9a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQFOLOCU3KS62323GEF6DQZHDI/bundle.json","state_url":"https://pith.science/pith/DQFOLOCU3KS62323GEF6DQZHDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQFOLOCU3KS62323GEF6DQZHDI/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":"2026-08-08T20:43:40Z","links":{"resolver":"https://pith.science/pith/DQFOLOCU3KS62323GEF6DQZHDI","bundle":"https://pith.science/pith/DQFOLOCU3KS62323GEF6DQZHDI/bundle.json","state":"https://pith.science/pith/DQFOLOCU3KS62323GEF6DQZHDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQFOLOCU3KS62323GEF6DQZHDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DQFOLOCU3KS62323GEF6DQZHDI","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":"cce34dbe4411dc6bce8c436b096adcc5dbdcafd4c68a03b0448df7cdda84180b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-02T21:54:36Z","title_canon_sha256":"81c58d7a0538788ed1c0a2329cd79218fd4f1c0bfc24116af5426fc1665cf9d0"},"schema_version":"1.0","source":{"id":"2403.01322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.01322","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"2403.01322v1","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.01322","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"DQFOLOCU3KS6","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"DQFOLOCU3KS62323","created_at":"2026-07-05T07:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"DQFOLOCU","created_at":"2026-07-05T07:51:45Z"}],"graph_snapshots":[{"event_id":"sha256:6b70edd050e8c98a7681c2503835ee9b67c1b8495b7024e4efa3c36cec09c9a5","target":"graph","created_at":"2026-07-05T07:51:45Z","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/2403.01322/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent (SGD) algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate $\\mathcal{O}(1/\\sqrt{nT})$ for smooth nonconvex functions, where $T$ and $n$ are the number of iterations and agents, respectively. If the global cost function additi","authors_text":"Antai Xie, Ming Cao, Xiaofan Wang, Xiaoqiang Ren, Xinlei Yi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-02T21:54:36Z","title":"A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.01322","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":"sha256:5a3c511e34b972181ead62ee1b809708ea6bb3d82f1dcd764d3efd92b5035607","target":"record","created_at":"2026-07-05T07:51:45Z","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":"cce34dbe4411dc6bce8c436b096adcc5dbdcafd4c68a03b0448df7cdda84180b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-02T21:54:36Z","title_canon_sha256":"81c58d7a0538788ed1c0a2329cd79218fd4f1c0bfc24116af5426fc1665cf9d0"},"schema_version":"1.0","source":{"id":"2403.01322","kind":"arxiv","version":1}},"canonical_sha256":"1c0ae5b854daa5ed6f5b310be1c3271a2ae8973441b4d689e76113d68ac49204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c0ae5b854daa5ed6f5b310be1c3271a2ae8973441b4d689e76113d68ac49204","first_computed_at":"2026-07-05T07:51:45.310827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:51:45.310827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNNa3mai1wwP5B7wMJ/d9fBzXm9FFuOJuavgJaJa/8ZdST8ycprktrc/SQklEoAm6G9LmVA4/UQzsf8jPH8RDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:51:45.311307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.01322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a3c511e34b972181ead62ee1b809708ea6bb3d82f1dcd764d3efd92b5035607","sha256:6b70edd050e8c98a7681c2503835ee9b67c1b8495b7024e4efa3c36cec09c9a5"],"state_sha256":"1f21fb268cb9f0edf1e02fed47fbc0f810249e9e9a3e40705af204111bdaa4b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vbeFdzoTA8Ow4MAMrmozFKCcWSBR6e/2SraVcp4CXK9W5DEHR9oMaffwiiGQbyl1fKAXRtmp22Ydgpkw7pVDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T20:43:40.613796Z","bundle_sha256":"6894d8771db62da3dc3c06dd51b0e2c75890c5fe2b6c213bc979b273bbc865eb"}}