{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KU7A2EVYTJ3WOSB3YP4X7ARREH","short_pith_number":"pith:KU7A2EVY","canonical_record":{"source":{"id":"2509.05213","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-05T16:15:22Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"d5ae58f51eae6370cdb764e789ec209687bf9f4db700f21cbaa9f94b8347a8dc","abstract_canon_sha256":"8bf5fb7c6c991baa9bf61e3732fa8650ff0506cde24957512a210fa8b6951fc7"},"schema_version":"1.0"},"canonical_sha256":"553e0d12b89a7767483bc3f97f823121e796249bc75315361705aca3e3195acd","source":{"kind":"arxiv","id":"2509.05213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05213","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05213v1","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05213","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"KU7A2EVYTJ3W","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"KU7A2EVYTJ3WOSB3","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"KU7A2EVY","created_at":"2026-07-05T12:05:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KU7A2EVYTJ3WOSB3YP4X7ARREH","target":"record","payload":{"canonical_record":{"source":{"id":"2509.05213","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-05T16:15:22Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"d5ae58f51eae6370cdb764e789ec209687bf9f4db700f21cbaa9f94b8347a8dc","abstract_canon_sha256":"8bf5fb7c6c991baa9bf61e3732fa8650ff0506cde24957512a210fa8b6951fc7"},"schema_version":"1.0"},"canonical_sha256":"553e0d12b89a7767483bc3f97f823121e796249bc75315361705aca3e3195acd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:05:37.903089Z","signature_b64":"puzruMEM56jUgH/HcygvupK5pWYW7yf2BTpDii9+m01iceKWCzv4BWZpP4cojZT1aYo+OkGjnrD/NQde2VdAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"553e0d12b89a7767483bc3f97f823121e796249bc75315361705aca3e3195acd","last_reissued_at":"2026-07-05T12:05:37.902576Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:05:37.902576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.05213","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":"2026-07-05T12:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3YURN7vYW0DGcnMEsUnxlWyKysJvc46GyJAo2WyQ675Snlws/6LUxRzeV3ilJ937fWBYKd/1Ha96CCU+S1BCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:33:47.653714Z"},"content_sha256":"eb745d7b4ef04cece275fcd7ec76c5d9674e20b0755fbf13da685a305a28dc4b","schema_version":"1.0","event_id":"sha256:eb745d7b4ef04cece275fcd7ec76c5d9674e20b0755fbf13da685a305a28dc4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KU7A2EVYTJ3WOSB3YP4X7ARREH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.LG","authors_text":"Jiaojiao Zhang, Kun Yuan, Yuqi Xu","submitted_at":"2025-09-05T16:15:22Z","abstract_excerpt":"This work addresses the key challenges of applying federated learning to large-scale deep neural networks, particularly the issue of client drift due to data heterogeneity across clients and the high costs of communication, computation, and memory. We propose FedSub, an efficient subspace algorithm for federated learning on heterogeneous data. Specifically, FedSub utilizes subspace projection to guarantee local updates of each client within low-dimensional subspaces, thereby reducing communication, computation, and memory costs. Additionally, it incorporates low-dimensional dual variables to m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05213","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/2509.05213/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":"2026-07-05T12:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogHPnp+dWgdAi//Wf7yre9c3E0x1it4tgOUA7ERYbG8iIU1zXT98Ypi+AEtrGQRAB3l/VwBeeFl2QZYXTJALAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:33:47.654593Z"},"content_sha256":"370f4c5e54b834c05e796bd8d789c7536b2ee797f011fa3f83e92a507c7412b3","schema_version":"1.0","event_id":"sha256:370f4c5e54b834c05e796bd8d789c7536b2ee797f011fa3f83e92a507c7412b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/bundle.json","state_url":"https://pith.science/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/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":"2026-08-05T12:33:47Z","links":{"resolver":"https://pith.science/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH","bundle":"https://pith.science/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/bundle.json","state":"https://pith.science/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KU7A2EVYTJ3WOSB3YP4X7ARREH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KU7A2EVYTJ3WOSB3YP4X7ARREH","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":"8bf5fb7c6c991baa9bf61e3732fa8650ff0506cde24957512a210fa8b6951fc7","cross_cats_sorted":["cs.DC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-05T16:15:22Z","title_canon_sha256":"d5ae58f51eae6370cdb764e789ec209687bf9f4db700f21cbaa9f94b8347a8dc"},"schema_version":"1.0","source":{"id":"2509.05213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05213","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05213v1","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05213","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"KU7A2EVYTJ3W","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"KU7A2EVYTJ3WOSB3","created_at":"2026-07-05T12:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"KU7A2EVY","created_at":"2026-07-05T12:05:37Z"}],"graph_snapshots":[{"event_id":"sha256:370f4c5e54b834c05e796bd8d789c7536b2ee797f011fa3f83e92a507c7412b3","target":"graph","created_at":"2026-07-05T12:05:37Z","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/2509.05213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work addresses the key challenges of applying federated learning to large-scale deep neural networks, particularly the issue of client drift due to data heterogeneity across clients and the high costs of communication, computation, and memory. We propose FedSub, an efficient subspace algorithm for federated learning on heterogeneous data. Specifically, FedSub utilizes subspace projection to guarantee local updates of each client within low-dimensional subspaces, thereby reducing communication, computation, and memory costs. Additionally, it incorporates low-dimensional dual variables to m","authors_text":"Jiaojiao Zhang, Kun Yuan, Yuqi Xu","cross_cats":["cs.DC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-05T16:15:22Z","title":"An Efficient Subspace Algorithm for Federated Learning on Heterogeneous Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05213","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:eb745d7b4ef04cece275fcd7ec76c5d9674e20b0755fbf13da685a305a28dc4b","target":"record","created_at":"2026-07-05T12:05:37Z","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":"8bf5fb7c6c991baa9bf61e3732fa8650ff0506cde24957512a210fa8b6951fc7","cross_cats_sorted":["cs.DC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-05T16:15:22Z","title_canon_sha256":"d5ae58f51eae6370cdb764e789ec209687bf9f4db700f21cbaa9f94b8347a8dc"},"schema_version":"1.0","source":{"id":"2509.05213","kind":"arxiv","version":1}},"canonical_sha256":"553e0d12b89a7767483bc3f97f823121e796249bc75315361705aca3e3195acd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"553e0d12b89a7767483bc3f97f823121e796249bc75315361705aca3e3195acd","first_computed_at":"2026-07-05T12:05:37.902576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:37.902576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"puzruMEM56jUgH/HcygvupK5pWYW7yf2BTpDii9+m01iceKWCzv4BWZpP4cojZT1aYo+OkGjnrD/NQde2VdAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:37.903089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb745d7b4ef04cece275fcd7ec76c5d9674e20b0755fbf13da685a305a28dc4b","sha256:370f4c5e54b834c05e796bd8d789c7536b2ee797f011fa3f83e92a507c7412b3"],"state_sha256":"ec0a4c2f1e23fa4be1cddd640bd1314cfef696307a13f55a3d5920044f2cb093"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQLTIv+0TURTOj/mhHqePxtIZoDlGSh9XNPl7SBX/jjCPi7m/8hR+RYcfE+4NDoJdVQe8qtNQIh1h0CPZv86Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T12:33:47.660556Z","bundle_sha256":"e25ba5890b923a3c808b9155083737206b4c4a5396e27f1f42a3ab0e57a5efb1"}}