{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FWDTLJMRR4GT6Y7OPHKEWCAWDR","short_pith_number":"pith:FWDTLJMR","canonical_record":{"source":{"id":"1907.09697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-23T05:15:55Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"910566c072b9d5429a2037989108dcb1f7886d1163f58e5e430e12762d3e1a7b","abstract_canon_sha256":"508a9039aa8eff5a4026520334b215f9cbbafff9192fb24d9f5a6a0fb7be79b1"},"schema_version":"1.0"},"canonical_sha256":"2d8735a5918f0d3f63ee79d44b08161c4f3f43fa4fb3669d321a16ec8f6b08bb","source":{"kind":"arxiv","id":"1907.09697","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09697","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09697v1","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09697","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"FWDTLJMRR4GT","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FWDTLJMRR4GT6Y7O","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FWDTLJMR","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FWDTLJMRR4GT6Y7OPHKEWCAWDR","target":"record","payload":{"canonical_record":{"source":{"id":"1907.09697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-23T05:15:55Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"910566c072b9d5429a2037989108dcb1f7886d1163f58e5e430e12762d3e1a7b","abstract_canon_sha256":"508a9039aa8eff5a4026520334b215f9cbbafff9192fb24d9f5a6a0fb7be79b1"},"schema_version":"1.0"},"canonical_sha256":"2d8735a5918f0d3f63ee79d44b08161c4f3f43fa4fb3669d321a16ec8f6b08bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:50.379033Z","signature_b64":"p4Mypkg/dUkrnz4O7Sproon/CBAtKM8LU/tdO+KKm6g2lJCV3M5Cvw5cNbjh30xolgmzUKmkXGAsk61NNSjEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d8735a5918f0d3f63ee79d44b08161c4f3f43fa4fb3669d321a16ec8f6b08bb","last_reissued_at":"2026-05-17T23:39:50.378493Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:50.378493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.09697","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":"2026-05-17T23:39:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqiO1QG9Qw6iIELKiqpsL6a4Ew7uqCQDk+PH+bY8ychva0JEVWqotrE5pedHNGbSlr+Mughqy5BiJjXGt3x1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:44:37.729489Z"},"content_sha256":"c8735e23308a6a29e68e90cc4aaec33d8e7e53e3ace4af935c43442e1078f50c","schema_version":"1.0","event_id":"sha256:c8735e23308a6a29e68e90cc4aaec33d8e7e53e3ace4af935c43442e1078f50c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FWDTLJMRR4GT6Y7OPHKEWCAWDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-ball Algorithms Always Escape Saddle Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Dongsheng Li, Hao Jiang, Shengguo Li, Tao Sun, Yong Dou, Zhe Quan","submitted_at":"2019-07-23T05:15:55Z","abstract_excerpt":"Nonconvex optimization algorithms with random initialization have attracted increasing attention recently. It has been showed that many first-order methods always avoid saddle points with random starting points. In this paper, we answer a question: can the nonconvex heavy-ball algorithms with random initialization avoid saddle points? The answer is yes! Direct using the existing proof technique for the heavy-ball algorithms is hard due to that each iteration of the heavy-ball algorithm consists of current and last points. It is impossible to formulate the algorithms as iteration like xk+1= g(x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09697","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":"2026-05-17T23:39:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QduoY84J1xm1Rvfaj1JAbs7BbeqLby0w12lEC+ut5umlnxz8O3Qy3llJ05sVzkMTSyitWqCu5ocqSvvc4evdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:44:37.730135Z"},"content_sha256":"ed2ddd7f00b1409db55e0fc69d475976d4f797a1c3c3b1de87a86f08132e12a7","schema_version":"1.0","event_id":"sha256:ed2ddd7f00b1409db55e0fc69d475976d4f797a1c3c3b1de87a86f08132e12a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/bundle.json","state_url":"https://pith.science/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/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":"2026-05-26T12:44:37Z","links":{"resolver":"https://pith.science/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR","bundle":"https://pith.science/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/bundle.json","state":"https://pith.science/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWDTLJMRR4GT6Y7OPHKEWCAWDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FWDTLJMRR4GT6Y7OPHKEWCAWDR","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":"508a9039aa8eff5a4026520334b215f9cbbafff9192fb24d9f5a6a0fb7be79b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-23T05:15:55Z","title_canon_sha256":"910566c072b9d5429a2037989108dcb1f7886d1163f58e5e430e12762d3e1a7b"},"schema_version":"1.0","source":{"id":"1907.09697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09697","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09697v1","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09697","created_at":"2026-05-17T23:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"FWDTLJMRR4GT","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FWDTLJMRR4GT6Y7O","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FWDTLJMR","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:ed2ddd7f00b1409db55e0fc69d475976d4f797a1c3c3b1de87a86f08132e12a7","target":"graph","created_at":"2026-05-17T23:39:50Z","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":"Nonconvex optimization algorithms with random initialization have attracted increasing attention recently. It has been showed that many first-order methods always avoid saddle points with random starting points. In this paper, we answer a question: can the nonconvex heavy-ball algorithms with random initialization avoid saddle points? The answer is yes! Direct using the existing proof technique for the heavy-ball algorithms is hard due to that each iteration of the heavy-ball algorithm consists of current and last points. It is impossible to formulate the algorithms as iteration like xk+1= g(x","authors_text":"Dongsheng Li, Hao Jiang, Shengguo Li, Tao Sun, Yong Dou, Zhe Quan","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-23T05:15:55Z","title":"Heavy-ball Algorithms Always Escape Saddle Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09697","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:c8735e23308a6a29e68e90cc4aaec33d8e7e53e3ace4af935c43442e1078f50c","target":"record","created_at":"2026-05-17T23:39:50Z","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":"508a9039aa8eff5a4026520334b215f9cbbafff9192fb24d9f5a6a0fb7be79b1","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-23T05:15:55Z","title_canon_sha256":"910566c072b9d5429a2037989108dcb1f7886d1163f58e5e430e12762d3e1a7b"},"schema_version":"1.0","source":{"id":"1907.09697","kind":"arxiv","version":1}},"canonical_sha256":"2d8735a5918f0d3f63ee79d44b08161c4f3f43fa4fb3669d321a16ec8f6b08bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d8735a5918f0d3f63ee79d44b08161c4f3f43fa4fb3669d321a16ec8f6b08bb","first_computed_at":"2026-05-17T23:39:50.378493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:50.378493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p4Mypkg/dUkrnz4O7Sproon/CBAtKM8LU/tdO+KKm6g2lJCV3M5Cvw5cNbjh30xolgmzUKmkXGAsk61NNSjEDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:50.379033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8735e23308a6a29e68e90cc4aaec33d8e7e53e3ace4af935c43442e1078f50c","sha256:ed2ddd7f00b1409db55e0fc69d475976d4f797a1c3c3b1de87a86f08132e12a7"],"state_sha256":"d2632d576308f43c6b006346bb9bc29b62a8ea0565dc5071bf5ebb16dac813f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9UmPNcBpLRtPZEk9a9ch2yBi+le70D48m1fiTJVIEO7bGS8i9FZXxwA+qFHfX3UW240MK3l5L0Axzfqk5QlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:44:37.733649Z","bundle_sha256":"1dcbd79d6996c981f690bd76593153abafef36b9d0c9d242a66968ebabffbdb7"}}