{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6GG4GJVTD43WJJHDOJUYKDQBBJ","short_pith_number":"pith:6GG4GJVT","canonical_record":{"source":{"id":"1410.0576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-02T14:49:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3a34428e54a58031ebebcf42fb344178516c82fc55464946e7f8c0807c91698d","abstract_canon_sha256":"689dafbe846499157a18fbd865e8e8ee1928326a654b1becc7f20965a0aa55f3"},"schema_version":"1.0"},"canonical_sha256":"f18dc326b31f3764a4e37269850e010a4714595db47e8dd71d29835005b1d25b","source":{"kind":"arxiv","id":"1410.0576","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0576","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0576v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0576","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"6GG4GJVTD43W","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6GG4GJVTD43WJJHD","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6GG4GJVT","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6GG4GJVTD43WJJHDOJUYKDQBBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-02T14:49:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"3a34428e54a58031ebebcf42fb344178516c82fc55464946e7f8c0807c91698d","abstract_canon_sha256":"689dafbe846499157a18fbd865e8e8ee1928326a654b1becc7f20965a0aa55f3"},"schema_version":"1.0"},"canonical_sha256":"f18dc326b31f3764a4e37269850e010a4714595db47e8dd71d29835005b1d25b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:10.689700Z","signature_b64":"pOewf7oST3bQ0LyXTiznkbgEjScCk2xo/MlpUcqWQT8IyAoQeyMEu185CAL54le3NmpjS5hDtZx4FwAO/298Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f18dc326b31f3764a4e37269850e010a4714595db47e8dd71d29835005b1d25b","last_reissued_at":"2026-05-18T02:41:10.689132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:10.689132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0576","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ezjta13SnC+lx2DPV2pUY1d3Hnc5nGLHuD+qjItTkV1jlMM01QaD3oNg9vIUJ2dFkYS845Xn8FfEu+6Bar3OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:41:36.159097Z"},"content_sha256":"b47b098dcf013ac28ce020c8d6eb94585762eec65ddad72878e4b54020ff3ef7","schema_version":"1.0","event_id":"sha256:b47b098dcf013ac28ce020c8d6eb94585762eec65ddad72878e4b54020ff3ef7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6GG4GJVTD43WJJHDOJUYKDQBBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mapping Energy Landscapes of Non-Convex Learning Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Kewei Tu, Maria Pavlovskaia, Song-Chun Zhu","submitted_at":"2014-10-02T14:49:59Z","abstract_excerpt":"In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \\emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node represents a local minimum and each non-leaf node represents the barrier between adjacent energy basins. The ELM also associates each node with the estimated probability mass and volume for the corresponding energy basin. We construct ELMs by adopting the generalized Wang-Landau al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0576","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":"2026-05-18T02:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWs7DLNuOO1VHX5roRLypk7W3EQrac95bJzxVviwP02LA1Z4HfVpFrZynxZ8q0uxumQl2/IcF3H2sqX6wFDQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:41:36.159589Z"},"content_sha256":"63c08311f51a77e6e38e3e1bc34b3ceb8ff23c3586df18830ba6ba6c18691bb4","schema_version":"1.0","event_id":"sha256:63c08311f51a77e6e38e3e1bc34b3ceb8ff23c3586df18830ba6ba6c18691bb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/bundle.json","state_url":"https://pith.science/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/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":"2026-06-24T23:41:36Z","links":{"resolver":"https://pith.science/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ","bundle":"https://pith.science/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/bundle.json","state":"https://pith.science/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GG4GJVTD43WJJHDOJUYKDQBBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6GG4GJVTD43WJJHDOJUYKDQBBJ","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":"689dafbe846499157a18fbd865e8e8ee1928326a654b1becc7f20965a0aa55f3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-02T14:49:59Z","title_canon_sha256":"3a34428e54a58031ebebcf42fb344178516c82fc55464946e7f8c0807c91698d"},"schema_version":"1.0","source":{"id":"1410.0576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0576","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0576v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0576","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"6GG4GJVTD43W","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6GG4GJVTD43WJJHD","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6GG4GJVT","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:63c08311f51a77e6e38e3e1bc34b3ceb8ff23c3586df18830ba6ba6c18691bb4","target":"graph","created_at":"2026-05-18T02:41:10Z","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 many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \\emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node represents a local minimum and each non-leaf node represents the barrier between adjacent energy basins. The ELM also associates each node with the estimated probability mass and volume for the corresponding energy basin. We construct ELMs by adopting the generalized Wang-Landau al","authors_text":"Kewei Tu, Maria Pavlovskaia, Song-Chun Zhu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-02T14:49:59Z","title":"Mapping Energy Landscapes of Non-Convex Learning Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0576","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:b47b098dcf013ac28ce020c8d6eb94585762eec65ddad72878e4b54020ff3ef7","target":"record","created_at":"2026-05-18T02:41:10Z","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":"689dafbe846499157a18fbd865e8e8ee1928326a654b1becc7f20965a0aa55f3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-02T14:49:59Z","title_canon_sha256":"3a34428e54a58031ebebcf42fb344178516c82fc55464946e7f8c0807c91698d"},"schema_version":"1.0","source":{"id":"1410.0576","kind":"arxiv","version":1}},"canonical_sha256":"f18dc326b31f3764a4e37269850e010a4714595db47e8dd71d29835005b1d25b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f18dc326b31f3764a4e37269850e010a4714595db47e8dd71d29835005b1d25b","first_computed_at":"2026-05-18T02:41:10.689132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:10.689132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pOewf7oST3bQ0LyXTiznkbgEjScCk2xo/MlpUcqWQT8IyAoQeyMEu185CAL54le3NmpjS5hDtZx4FwAO/298Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:10.689700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b47b098dcf013ac28ce020c8d6eb94585762eec65ddad72878e4b54020ff3ef7","sha256:63c08311f51a77e6e38e3e1bc34b3ceb8ff23c3586df18830ba6ba6c18691bb4"],"state_sha256":"02239eea65644244f4f6db1401cd83fa02252617d0bee4aa3e8d2c8e01efe3da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJ6DvYnyC09G9NjC+g8fDlR2dKjFFntcd7ES+wuRtEjg7qcFujq2USWY2pdp/vP1Zn7K4yTFx2ZsVZNOcQENAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:41:36.162160Z","bundle_sha256":"35626afceabd5430407f57ae21203dc1e95caa6308b875bc5ac5ea24aee92547"}}