{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RVNEDY4UE5QKTHCXSHDVBCEXSR","short_pith_number":"pith:RVNEDY4U","canonical_record":{"source":{"id":"2306.11922","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-06-20T22:10:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ddec7eac1e2a027d8c3ae9938640d99896a82f826d932754f8641ed003922e7c","abstract_canon_sha256":"359bd16cb3ff6d2bef3f33caed2e40b76cf38d2f77c3b310b5ad953d0e8249b8"},"schema_version":"1.0"},"canonical_sha256":"8d5a41e3942760a99c5791c750889794563bbe945d0f4dafd5b7f762408fe7e8","source":{"kind":"arxiv","id":"2306.11922","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.11922","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2306.11922v1","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11922","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"RVNEDY4UE5QK","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"RVNEDY4UE5QKTHCX","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"RVNEDY4U","created_at":"2026-07-05T06:23:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RVNEDY4UE5QKTHCXSHDVBCEXSR","target":"record","payload":{"canonical_record":{"source":{"id":"2306.11922","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-06-20T22:10:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ddec7eac1e2a027d8c3ae9938640d99896a82f826d932754f8641ed003922e7c","abstract_canon_sha256":"359bd16cb3ff6d2bef3f33caed2e40b76cf38d2f77c3b310b5ad953d0e8249b8"},"schema_version":"1.0"},"canonical_sha256":"8d5a41e3942760a99c5791c750889794563bbe945d0f4dafd5b7f762408fe7e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:08.561844Z","signature_b64":"dpPJzU0e/QIFkgdjflDv0zBwF96XJgtf7Q4tV/Ezl36zVZT/XWIwdL3wHNlQ6h3CoN4Rc+wDCCFGdAB0Cuw/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d5a41e3942760a99c5791c750889794563bbe945d0f4dafd5b7f762408fe7e8","last_reissued_at":"2026-07-05T06:23:08.561447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:08.561447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.11922","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":"2026-07-05T06:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikO33Jg7P/5kutDDs2jncY5uem0xz/TQd7ihyj8w4yg6mCves0uPwIQbz1EA/I8kUXTJBSENGz8bSIXQ9YjmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:39:29.811821Z"},"content_sha256":"7da61c96008a5091541c4aed86cdd16a836808e5b0a8dcb3b35df243e67e980d","schema_version":"1.0","event_id":"sha256:7da61c96008a5091541c4aed86cdd16a836808e5b0a8dcb3b35df243e67e980d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RVNEDY4UE5QKTHCXSHDVBCEXSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"No Wrong Turns: The Simple Geometry Of Neural Networks Optimization Paths","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Charles Guille-Escuret, Hiroki Naganuma, Ioannis Mitliagkas, Kilian Fatras","submitted_at":"2023-06-20T22:10:40Z","abstract_excerpt":"Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural networks. This efficiency, however, contrasts with the non-convex and seemingly complex structure of neural loss landscapes. In this study, we delve into the fundamental geometric properties of sampled gradients along optimization paths. We focus on two key quantities, which appear in the restricted secant inequality and error bound. Both hold high significance for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11922","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/2306.11922/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":"2026-07-05T06:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DdtQxttw3QLdBJ8v40Hmp7CyJGaxNt0xeP/YqdfARc3noY4gZgchVHaj4jZDbzrTA076nZHIGwbiywr8coPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:39:29.812414Z"},"content_sha256":"b69b224493d5d8b4146a750cb4b98cb13f3c3e3e259e152ccf5d8973f27bd9e6","schema_version":"1.0","event_id":"sha256:b69b224493d5d8b4146a750cb4b98cb13f3c3e3e259e152ccf5d8973f27bd9e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/bundle.json","state_url":"https://pith.science/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/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":"2026-08-07T17:39:29Z","links":{"resolver":"https://pith.science/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR","bundle":"https://pith.science/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/bundle.json","state":"https://pith.science/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVNEDY4UE5QKTHCXSHDVBCEXSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RVNEDY4UE5QKTHCXSHDVBCEXSR","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":"359bd16cb3ff6d2bef3f33caed2e40b76cf38d2f77c3b310b5ad953d0e8249b8","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-06-20T22:10:40Z","title_canon_sha256":"ddec7eac1e2a027d8c3ae9938640d99896a82f826d932754f8641ed003922e7c"},"schema_version":"1.0","source":{"id":"2306.11922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.11922","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2306.11922v1","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11922","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"RVNEDY4UE5QK","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"RVNEDY4UE5QKTHCX","created_at":"2026-07-05T06:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"RVNEDY4U","created_at":"2026-07-05T06:23:08Z"}],"graph_snapshots":[{"event_id":"sha256:b69b224493d5d8b4146a750cb4b98cb13f3c3e3e259e152ccf5d8973f27bd9e6","target":"graph","created_at":"2026-07-05T06:23:08Z","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/2306.11922/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural networks. This efficiency, however, contrasts with the non-convex and seemingly complex structure of neural loss landscapes. In this study, we delve into the fundamental geometric properties of sampled gradients along optimization paths. We focus on two key quantities, which appear in the restricted secant inequality and error bound. Both hold high significance for ","authors_text":"Charles Guille-Escuret, Hiroki Naganuma, Ioannis Mitliagkas, Kilian Fatras","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-06-20T22:10:40Z","title":"No Wrong Turns: The Simple Geometry Of Neural Networks Optimization Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11922","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":"sha256:7da61c96008a5091541c4aed86cdd16a836808e5b0a8dcb3b35df243e67e980d","target":"record","created_at":"2026-07-05T06:23:08Z","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":"359bd16cb3ff6d2bef3f33caed2e40b76cf38d2f77c3b310b5ad953d0e8249b8","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-06-20T22:10:40Z","title_canon_sha256":"ddec7eac1e2a027d8c3ae9938640d99896a82f826d932754f8641ed003922e7c"},"schema_version":"1.0","source":{"id":"2306.11922","kind":"arxiv","version":1}},"canonical_sha256":"8d5a41e3942760a99c5791c750889794563bbe945d0f4dafd5b7f762408fe7e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d5a41e3942760a99c5791c750889794563bbe945d0f4dafd5b7f762408fe7e8","first_computed_at":"2026-07-05T06:23:08.561447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:08.561447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dpPJzU0e/QIFkgdjflDv0zBwF96XJgtf7Q4tV/Ezl36zVZT/XWIwdL3wHNlQ6h3CoN4Rc+wDCCFGdAB0Cuw/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:08.561844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.11922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7da61c96008a5091541c4aed86cdd16a836808e5b0a8dcb3b35df243e67e980d","sha256:b69b224493d5d8b4146a750cb4b98cb13f3c3e3e259e152ccf5d8973f27bd9e6"],"state_sha256":"5a22426f3682bc19060004252b4b45696150d6044244f3340b91c48f483c1af7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAogdWFwVR8wHLYQJ6vubhBsgn7BVHIN78jOw/KhgnNDvIhALVIA4y/ZGeh9rb4YyHZ5wvLoZ1RaFlhXG9hPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T17:39:29.817696Z","bundle_sha256":"db8c0872b958018736c2340ba2d98ead4f6b09fbed2054c1d090de85f59bda81"}}