{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NT6KBH5XWY4NI4JD5SUQFGAXUU","short_pith_number":"pith:NT6KBH5X","canonical_record":{"source":{"id":"2509.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-14T12:54:28Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b85f6f725d249ad32b02717b408b0448f412db4c9e34e715c3fe0ebc9d25dbb0","abstract_canon_sha256":"8f61617d52f24cbcb2e8a41528255742750208fca48ab7ab8c95aa5742479282"},"schema_version":"1.0"},"canonical_sha256":"6cfca09fb7b638d47123eca9029817a51960c773ab2d743304316bab81552eb9","source":{"kind":"arxiv","id":"2509.11254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.11254","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"arxiv_version","alias_value":"2509.11254v1","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11254","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_12","alias_value":"NT6KBH5XWY4N","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_16","alias_value":"NT6KBH5XWY4NI4JD","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_8","alias_value":"NT6KBH5X","created_at":"2026-07-05T12:11:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NT6KBH5XWY4NI4JD5SUQFGAXUU","target":"record","payload":{"canonical_record":{"source":{"id":"2509.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-14T12:54:28Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b85f6f725d249ad32b02717b408b0448f412db4c9e34e715c3fe0ebc9d25dbb0","abstract_canon_sha256":"8f61617d52f24cbcb2e8a41528255742750208fca48ab7ab8c95aa5742479282"},"schema_version":"1.0"},"canonical_sha256":"6cfca09fb7b638d47123eca9029817a51960c773ab2d743304316bab81552eb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:11:36.190608Z","signature_b64":"uqXRz6SzlHp81mF973E9RQDauH1oJ+4oTbXoX5SQ+2wDUu7J1OPAwhrIFtZgaM2J4Y47MA6uim5G9BWj6ib2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cfca09fb7b638d47123eca9029817a51960c773ab2d743304316bab81552eb9","last_reissued_at":"2026-07-05T12:11:36.190135Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:11:36.190135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.11254","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":"2026-07-05T12:11:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3UOS3DCEpynjPPrJmMte7PTta7zE8AdCWO4pIAFFS52C641qCotO6xmQe83KkPaivRUpRVzKR9Dy7MrIaIgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:22:06.756291Z"},"content_sha256":"53fdcb256268bada3c3d4443858075357f734494942d8a2ee62e45fe47c1c997","schema_version":"1.0","event_id":"sha256:53fdcb256268bada3c3d4443858075357f734494942d8a2ee62e45fe47c1c997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NT6KBH5XWY4NI4JD5SUQFGAXUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From PowerSGD to PowerSGD+: Low-Rank Gradient Compression for Distributed Optimization with Convergence Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Chuyan Chen, Kun Yuan, Shengping Xie","submitted_at":"2025-09-14T12:54:28Z","abstract_excerpt":"Low-rank gradient compression methods, such as PowerSGD, have gained attention in communication-efficient distributed optimization. However, the convergence guarantees of PowerSGD remain unclear, particularly in stochastic settings. In this paper, we show that PowerSGD does not always converge to the optimal solution and provide a clear counterexample to support this finding. To address this, we introduce PowerSGD+, which periodically updates the projection subspace via singular value decomposition, ensuring that it remains aligned with the optimal subspace. We prove that PowerSGD+ converges u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11254","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/2509.11254/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":"2026-07-05T12:11:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maEftABfleXUNJ2m4IFnX87NpGeCFN8qdH2d4d/lbtO5BzLmWLwWXxgASecTmk60opoqobj4ZISF9gdEV2o1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:22:06.756808Z"},"content_sha256":"801fb73cc8b3ba12240bb0fa548c7ec38cf4be34e83d586d6b2ff057f8aa8868","schema_version":"1.0","event_id":"sha256:801fb73cc8b3ba12240bb0fa548c7ec38cf4be34e83d586d6b2ff057f8aa8868"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/bundle.json","state_url":"https://pith.science/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/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":"2026-08-06T06:22:06Z","links":{"resolver":"https://pith.science/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU","bundle":"https://pith.science/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/bundle.json","state":"https://pith.science/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NT6KBH5XWY4NI4JD5SUQFGAXUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NT6KBH5XWY4NI4JD5SUQFGAXUU","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":"8f61617d52f24cbcb2e8a41528255742750208fca48ab7ab8c95aa5742479282","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-14T12:54:28Z","title_canon_sha256":"b85f6f725d249ad32b02717b408b0448f412db4c9e34e715c3fe0ebc9d25dbb0"},"schema_version":"1.0","source":{"id":"2509.11254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.11254","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"arxiv_version","alias_value":"2509.11254v1","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11254","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_12","alias_value":"NT6KBH5XWY4N","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_16","alias_value":"NT6KBH5XWY4NI4JD","created_at":"2026-07-05T12:11:36Z"},{"alias_kind":"pith_short_8","alias_value":"NT6KBH5X","created_at":"2026-07-05T12:11:36Z"}],"graph_snapshots":[{"event_id":"sha256:801fb73cc8b3ba12240bb0fa548c7ec38cf4be34e83d586d6b2ff057f8aa8868","target":"graph","created_at":"2026-07-05T12:11:36Z","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/2509.11254/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-rank gradient compression methods, such as PowerSGD, have gained attention in communication-efficient distributed optimization. However, the convergence guarantees of PowerSGD remain unclear, particularly in stochastic settings. In this paper, we show that PowerSGD does not always converge to the optimal solution and provide a clear counterexample to support this finding. To address this, we introduce PowerSGD+, which periodically updates the projection subspace via singular value decomposition, ensuring that it remains aligned with the optimal subspace. We prove that PowerSGD+ converges u","authors_text":"Chuyan Chen, Kun Yuan, Shengping Xie","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-14T12:54:28Z","title":"From PowerSGD to PowerSGD+: Low-Rank Gradient Compression for Distributed Optimization with Convergence Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11254","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":"sha256:53fdcb256268bada3c3d4443858075357f734494942d8a2ee62e45fe47c1c997","target":"record","created_at":"2026-07-05T12:11:36Z","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":"8f61617d52f24cbcb2e8a41528255742750208fca48ab7ab8c95aa5742479282","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-09-14T12:54:28Z","title_canon_sha256":"b85f6f725d249ad32b02717b408b0448f412db4c9e34e715c3fe0ebc9d25dbb0"},"schema_version":"1.0","source":{"id":"2509.11254","kind":"arxiv","version":1}},"canonical_sha256":"6cfca09fb7b638d47123eca9029817a51960c773ab2d743304316bab81552eb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cfca09fb7b638d47123eca9029817a51960c773ab2d743304316bab81552eb9","first_computed_at":"2026-07-05T12:11:36.190135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:11:36.190135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uqXRz6SzlHp81mF973E9RQDauH1oJ+4oTbXoX5SQ+2wDUu7J1OPAwhrIFtZgaM2J4Y47MA6uim5G9BWj6ib2AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:11:36.190608Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.11254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53fdcb256268bada3c3d4443858075357f734494942d8a2ee62e45fe47c1c997","sha256:801fb73cc8b3ba12240bb0fa548c7ec38cf4be34e83d586d6b2ff057f8aa8868"],"state_sha256":"75a4f92cf6bbbaaa7750885bf6ca8199874b6b013a534aa4924200f0383d3923"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvMq2kMVEgjqQdVIcDXQB2qH8SkNfLnh19yIxuxqZ31VPVsGtMbNVTzC5Vka3IugRS52vi10a6LPb08iYrwrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:22:06.760719Z","bundle_sha256":"0f5db9af11530d6b806f92ce5a2cd50b36093efce1c7a8b0c86e144230b845d6"}}