{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6HHK2YLPODHIEIMA6FIUFSPZ55","short_pith_number":"pith:6HHK2YLP","canonical_record":{"source":{"id":"1705.09059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-25T06:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"27b8ce0a910e293329bc0a28c0b28d6ad7029ede3a83b99d40a1618677e43ba5","abstract_canon_sha256":"f6db8c4da76e256f573f8d01d9cb3cbfc36491b6705161e83189c9d404bc27f0"},"schema_version":"1.0"},"canonical_sha256":"f1cead616f70ce822180f15142c9f9ef5277bcb6a71929d6008fb4aa60eaa9bb","source":{"kind":"arxiv","id":"1705.09059","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09059","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09059v1","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09059","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"pith_short_12","alias_value":"6HHK2YLPODHI","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6HHK2YLPODHIEIMA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6HHK2YLP","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6HHK2YLPODHIEIMA6FIUFSPZ55","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-25T06:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"27b8ce0a910e293329bc0a28c0b28d6ad7029ede3a83b99d40a1618677e43ba5","abstract_canon_sha256":"f6db8c4da76e256f573f8d01d9cb3cbfc36491b6705161e83189c9d404bc27f0"},"schema_version":"1.0"},"canonical_sha256":"f1cead616f70ce822180f15142c9f9ef5277bcb6a71929d6008fb4aa60eaa9bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:40.520967Z","signature_b64":"3VG9HFYyLTwVyC4fSiqNaJD0MPgYpw4+iZxLwAJieIuBivden4sgq/7RhXo6e7YJjXgNOklw2izLo68uI63TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1cead616f70ce822180f15142c9f9ef5277bcb6a71929d6008fb4aa60eaa9bb","last_reissued_at":"2026-05-18T00:43:40.520419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:40.520419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09059","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":"2026-05-18T00:43:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vm+IRd6c0Bd6zGzjAS/3+l2HJZP80rVUG3MjmeQcmoq5dmY1SBgRi1gffieGL135sRCVUcP8tMcHp4vzUMplBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:08:15.354517Z"},"content_sha256":"a087f77e668b7053c712a3a7e3658adf52c21561ac873ebd2a9d80b213c254f4","schema_version":"1.0","event_id":"sha256:a087f77e668b7053c712a3a7e3658adf52c21561ac873ebd2a9d80b213c254f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6HHK2YLPODHIEIMA6FIUFSPZ55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anthony Man-Cho So, Bo Jiang, Shiqian Ma, Shuzhong Zhang","submitted_at":"2017-05-25T06:22:37Z","abstract_excerpt":"In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we propose in this paper handles general retraction operations, and do not need additional computational costs mentioned above. As a result, we name our algorithm S-SVRG, where the first "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09059","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":"2026-05-18T00:43:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pv2O85tslwzIYu5GWIK2EzDUD+mVnizHGV3MN0tc4rsC3x80hYRkVR1k5ULnIkx/T6+D3YtNDnCPbtBdKRF0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:08:15.354879Z"},"content_sha256":"b98cfa64eb1262346bbcea13ade08e9c3da758878ccef67b35c93a5fd478b1a7","schema_version":"1.0","event_id":"sha256:b98cfa64eb1262346bbcea13ade08e9c3da758878ccef67b35c93a5fd478b1a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/bundle.json","state_url":"https://pith.science/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/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":"2026-05-28T11:08:15Z","links":{"resolver":"https://pith.science/pith/6HHK2YLPODHIEIMA6FIUFSPZ55","bundle":"https://pith.science/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/bundle.json","state":"https://pith.science/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HHK2YLPODHIEIMA6FIUFSPZ55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6HHK2YLPODHIEIMA6FIUFSPZ55","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":"f6db8c4da76e256f573f8d01d9cb3cbfc36491b6705161e83189c9d404bc27f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-25T06:22:37Z","title_canon_sha256":"27b8ce0a910e293329bc0a28c0b28d6ad7029ede3a83b99d40a1618677e43ba5"},"schema_version":"1.0","source":{"id":"1705.09059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09059","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09059v1","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09059","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"pith_short_12","alias_value":"6HHK2YLPODHI","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6HHK2YLPODHIEIMA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6HHK2YLP","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b98cfa64eb1262346bbcea13ade08e9c3da758878ccef67b35c93a5fd478b1a7","target":"graph","created_at":"2026-05-18T00:43:40Z","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":"In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we propose in this paper handles general retraction operations, and do not need additional computational costs mentioned above. As a result, we name our algorithm S-SVRG, where the first ","authors_text":"Anthony Man-Cho So, Bo Jiang, Shiqian Ma, Shuzhong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-25T06:22:37Z","title":"Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09059","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:a087f77e668b7053c712a3a7e3658adf52c21561ac873ebd2a9d80b213c254f4","target":"record","created_at":"2026-05-18T00:43:40Z","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":"f6db8c4da76e256f573f8d01d9cb3cbfc36491b6705161e83189c9d404bc27f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-25T06:22:37Z","title_canon_sha256":"27b8ce0a910e293329bc0a28c0b28d6ad7029ede3a83b99d40a1618677e43ba5"},"schema_version":"1.0","source":{"id":"1705.09059","kind":"arxiv","version":1}},"canonical_sha256":"f1cead616f70ce822180f15142c9f9ef5277bcb6a71929d6008fb4aa60eaa9bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1cead616f70ce822180f15142c9f9ef5277bcb6a71929d6008fb4aa60eaa9bb","first_computed_at":"2026-05-18T00:43:40.520419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:40.520419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3VG9HFYyLTwVyC4fSiqNaJD0MPgYpw4+iZxLwAJieIuBivden4sgq/7RhXo6e7YJjXgNOklw2izLo68uI63TAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:40.520967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a087f77e668b7053c712a3a7e3658adf52c21561ac873ebd2a9d80b213c254f4","sha256:b98cfa64eb1262346bbcea13ade08e9c3da758878ccef67b35c93a5fd478b1a7"],"state_sha256":"6647f3f0e79f28c65fecd07e0346fcf78ae2d9ac8e5e022d57c5b8f2da1508a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQO6asxkbKenbJB4HRJOB02PYg9b+w/Znb5qdV0zONYt9YT0QBY5ggEUG/pQaRZ9FVh5kEQ5qJo5HvoHb3a0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:08:15.356901Z","bundle_sha256":"a7e8daa51f519679630d5b08e21ffd72e06cffec481c14ea53736ef56faf5342"}}