{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3S5EJP32RX2IEWKOSHNDFWCKHP","short_pith_number":"pith:3S5EJP32","canonical_record":{"source":{"id":"1901.07417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-22T15:34:54Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3598edcad315389164691b469e7fbb195d05197f54cc366fd8f8413951d01203","abstract_canon_sha256":"72e4d94d7a04d45d7b757b5e5f9d3986e96270236d1c961290785e70461232e4"},"schema_version":"1.0"},"canonical_sha256":"dcba44bf7a8df482594e91da32d84a3be3102dc5e133f8f7ce5579c743c71e8f","source":{"kind":"arxiv","id":"1901.07417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07417","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07417v2","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07417","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"3S5EJP32RX2I","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3S5EJP32RX2IEWKO","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3S5EJP32","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3S5EJP32RX2IEWKOSHNDFWCKHP","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-22T15:34:54Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3598edcad315389164691b469e7fbb195d05197f54cc366fd8f8413951d01203","abstract_canon_sha256":"72e4d94d7a04d45d7b757b5e5f9d3986e96270236d1c961290785e70461232e4"},"schema_version":"1.0"},"canonical_sha256":"dcba44bf7a8df482594e91da32d84a3be3102dc5e133f8f7ce5579c743c71e8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:18.808058Z","signature_b64":"cfkezeE+eDaToGXP/7JAn0kVsGLllRe5/huSWLPHA2rZgr1HeROzI36Ox3z6GB4ZCq+C4NZlnuzuDf936kA6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcba44bf7a8df482594e91da32d84a3be3102dc5e133f8f7ce5579c743c71e8f","last_reissued_at":"2026-05-17T23:46:18.807234Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:18.807234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07417","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzQ/DM1cuw7WRsm5/Gb10sR/7fwwWXhm3lSeyBdo4+8kXaUWRT6daDFEDG6E4TkjoyKV1oOX8cMiS/htyKBNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:02.612846Z"},"content_sha256":"6a11de2e7aeecd982a5c313781043f3bb168035714508e987ce9b57924ebe967","schema_version":"1.0","event_id":"sha256:6a11de2e7aeecd982a5c313781043f3bb168035714508e987ce9b57924ebe967"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3S5EJP32RX2IEWKOSHNDFWCKHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Connected Sublevel Sets in Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Quynh Nguyen","submitted_at":"2019-01-22T15:34:54Z","abstract_excerpt":"This paper shows that every sublevel set of the loss function of a class of deep over-parameterized neural nets with piecewise linear activation functions is connected and unbounded. This implies that the loss has no bad local valleys and all of its global minima are connected within a unique and potentially very large global valley."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07417","kind":"arxiv","version":2},"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":"2026-05-17T23:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJHKxvO+o50MRlYpoNA137abKezWidhwzWhg4h0wH610obbEIwQZ61mFQsxCn/uJ94TE6kd2Wbl2b8S+eSf0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:52:02.613174Z"},"content_sha256":"220ae5faa1e7ab65edb19c8067b792919ae383850e0b1e61c39a8adc55c7b625","schema_version":"1.0","event_id":"sha256:220ae5faa1e7ab65edb19c8067b792919ae383850e0b1e61c39a8adc55c7b625"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/bundle.json","state_url":"https://pith.science/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/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":"2026-06-23T00:52:02Z","links":{"resolver":"https://pith.science/pith/3S5EJP32RX2IEWKOSHNDFWCKHP","bundle":"https://pith.science/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/bundle.json","state":"https://pith.science/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3S5EJP32RX2IEWKOSHNDFWCKHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3S5EJP32RX2IEWKOSHNDFWCKHP","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":"72e4d94d7a04d45d7b757b5e5f9d3986e96270236d1c961290785e70461232e4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-22T15:34:54Z","title_canon_sha256":"3598edcad315389164691b469e7fbb195d05197f54cc366fd8f8413951d01203"},"schema_version":"1.0","source":{"id":"1901.07417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07417","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07417v2","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07417","created_at":"2026-05-17T23:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"3S5EJP32RX2I","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3S5EJP32RX2IEWKO","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3S5EJP32","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:220ae5faa1e7ab65edb19c8067b792919ae383850e0b1e61c39a8adc55c7b625","target":"graph","created_at":"2026-05-17T23:46:18Z","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":"This paper shows that every sublevel set of the loss function of a class of deep over-parameterized neural nets with piecewise linear activation functions is connected and unbounded. This implies that the loss has no bad local valleys and all of its global minima are connected within a unique and potentially very large global valley.","authors_text":"Quynh Nguyen","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-22T15:34:54Z","title":"On Connected Sublevel Sets in Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07417","kind":"arxiv","version":2},"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":"sha256:6a11de2e7aeecd982a5c313781043f3bb168035714508e987ce9b57924ebe967","target":"record","created_at":"2026-05-17T23:46:18Z","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":"72e4d94d7a04d45d7b757b5e5f9d3986e96270236d1c961290785e70461232e4","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-22T15:34:54Z","title_canon_sha256":"3598edcad315389164691b469e7fbb195d05197f54cc366fd8f8413951d01203"},"schema_version":"1.0","source":{"id":"1901.07417","kind":"arxiv","version":2}},"canonical_sha256":"dcba44bf7a8df482594e91da32d84a3be3102dc5e133f8f7ce5579c743c71e8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcba44bf7a8df482594e91da32d84a3be3102dc5e133f8f7ce5579c743c71e8f","first_computed_at":"2026-05-17T23:46:18.807234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:18.807234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cfkezeE+eDaToGXP/7JAn0kVsGLllRe5/huSWLPHA2rZgr1HeROzI36Ox3z6GB4ZCq+C4NZlnuzuDf936kA6Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:18.808058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a11de2e7aeecd982a5c313781043f3bb168035714508e987ce9b57924ebe967","sha256:220ae5faa1e7ab65edb19c8067b792919ae383850e0b1e61c39a8adc55c7b625"],"state_sha256":"240e00e692014819bf84638bfc394a769fc5f2364cce973e5c3bda6daf1361d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jzaqf6bXwlNQfmCNRuZyLxmRZYMFfrTgPMjPM+hcgeW0nGHZRgM83KikInJBGArxQ76Vh3NKBWgtybuxgCk5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:52:02.615142Z","bundle_sha256":"6aa64dec5e72461c32f9850c397418eb8ff992779dec37429000036480411153"}}