{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3GJPOCCPX7NA5MUFSBZMLMLTM4","short_pith_number":"pith:3GJPOCCP","canonical_record":{"source":{"id":"1612.09034","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-29T04:25:28Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"005459c12ff31978e2086f2580fca3083bea83d6d6a8cc55e7a3f8c80e4b99c7","abstract_canon_sha256":"6767a81de872f58d2653c926adceb5a30d7ca4b0edcfa51ff0728df34f6e875c"},"schema_version":"1.0"},"canonical_sha256":"d992f7084fbfda0eb2859072c5b1736701d4ae633c1239a3d70bf314ccb412b4","source":{"kind":"arxiv","id":"1612.09034","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09034","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09034v4","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09034","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"3GJPOCCPX7NA","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3GJPOCCPX7NA5MUF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3GJPOCCP","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3GJPOCCPX7NA5MUFSBZMLMLTM4","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09034","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-29T04:25:28Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"005459c12ff31978e2086f2580fca3083bea83d6d6a8cc55e7a3f8c80e4b99c7","abstract_canon_sha256":"6767a81de872f58d2653c926adceb5a30d7ca4b0edcfa51ff0728df34f6e875c"},"schema_version":"1.0"},"canonical_sha256":"d992f7084fbfda0eb2859072c5b1736701d4ae633c1239a3d70bf314ccb412b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:29.440445Z","signature_b64":"mm7QO6HE24bghnqnp9DxAxD3sPG+Jw4UGQq7OMORSGXNlDf+77ePfYsp3WNrx764SHipzGVkVT6GJKCjhUYyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d992f7084fbfda0eb2859072c5b1736701d4ae633c1239a3d70bf314ccb412b4","last_reissued_at":"2026-05-18T00:43:29.439771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:29.439771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09034","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":"2026-05-18T00:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDxpQlpq5jpUW6RgzdUsBDwvlU6qsuNSXjgYvTsibH58pq7YurfHpAt1nCBelb6UFGi+gW2NGh19u7usjwtKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:12:24.370552Z"},"content_sha256":"38deed3603d09c4a7195d04a5687c9718c0498798dee94eac9deec2c73cc92cb","schema_version":"1.0","event_id":"sha256:38deed3603d09c4a7195d04a5687c9718c0498798dee94eac9deec2c73cc92cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3GJPOCCPX7NA5MUFSBZMLMLTM4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric descent method for convex composite minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Shiqian Ma, Shixiang Chen, Wei Liu","submitted_at":"2016-12-29T04:25:28Z","abstract_excerpt":"In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\\sqrt{\\kappa})$ and thus achieves the optimal rate among first-order methods, where $\\kappa$ is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09034","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":""},"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":"2026-05-18T00:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xt/i9UDyYKXitcjXGPZdLTLDRJgOiCfhyoHwemb9sTXIF93teC/EQ2pIZ2hnQbUJ52JnYM7uz5uvZopZC3IEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:12:24.371281Z"},"content_sha256":"2bdc7541b25f390b075192474e86bb066dbe7d4c10e36782614f51237e1d8a17","schema_version":"1.0","event_id":"sha256:2bdc7541b25f390b075192474e86bb066dbe7d4c10e36782614f51237e1d8a17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/bundle.json","state_url":"https://pith.science/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/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":"2026-06-11T07:12:24Z","links":{"resolver":"https://pith.science/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4","bundle":"https://pith.science/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/bundle.json","state":"https://pith.science/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GJPOCCPX7NA5MUFSBZMLMLTM4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3GJPOCCPX7NA5MUFSBZMLMLTM4","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":"6767a81de872f58d2653c926adceb5a30d7ca4b0edcfa51ff0728df34f6e875c","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-29T04:25:28Z","title_canon_sha256":"005459c12ff31978e2086f2580fca3083bea83d6d6a8cc55e7a3f8c80e4b99c7"},"schema_version":"1.0","source":{"id":"1612.09034","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09034","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09034v4","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09034","created_at":"2026-05-18T00:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"3GJPOCCPX7NA","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3GJPOCCPX7NA5MUF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3GJPOCCP","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:2bdc7541b25f390b075192474e86bb066dbe7d4c10e36782614f51237e1d8a17","target":"graph","created_at":"2026-05-18T00:43:29Z","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 extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\\sqrt{\\kappa})$ and thus achieves the optimal rate among first-order methods, where $\\kappa$ is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, es","authors_text":"Shiqian Ma, Shixiang Chen, Wei Liu","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-29T04:25:28Z","title":"Geometric descent method for convex composite minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09034","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":"sha256:38deed3603d09c4a7195d04a5687c9718c0498798dee94eac9deec2c73cc92cb","target":"record","created_at":"2026-05-18T00:43:29Z","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":"6767a81de872f58d2653c926adceb5a30d7ca4b0edcfa51ff0728df34f6e875c","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-29T04:25:28Z","title_canon_sha256":"005459c12ff31978e2086f2580fca3083bea83d6d6a8cc55e7a3f8c80e4b99c7"},"schema_version":"1.0","source":{"id":"1612.09034","kind":"arxiv","version":4}},"canonical_sha256":"d992f7084fbfda0eb2859072c5b1736701d4ae633c1239a3d70bf314ccb412b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d992f7084fbfda0eb2859072c5b1736701d4ae633c1239a3d70bf314ccb412b4","first_computed_at":"2026-05-18T00:43:29.439771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:29.439771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mm7QO6HE24bghnqnp9DxAxD3sPG+Jw4UGQq7OMORSGXNlDf+77ePfYsp3WNrx764SHipzGVkVT6GJKCjhUYyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:29.440445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09034","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38deed3603d09c4a7195d04a5687c9718c0498798dee94eac9deec2c73cc92cb","sha256:2bdc7541b25f390b075192474e86bb066dbe7d4c10e36782614f51237e1d8a17"],"state_sha256":"662815cc203bf364d2bd3ca85c1add0889eb7d44b7085c7fdd7bc47598da5328"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XZmQDqNHBLenaC09MCYDvdW7yHVkCBHRYgdbulhrqx4Ej3zAjaq4/IQh9qOVm0ZpW40vavQigXtjzmToTVoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:12:24.375801Z","bundle_sha256":"9dd4746467d876d8aa3eb8c72c7860b48687d71d280bbad95f29c59d2a5cc20d"}}