{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:2QLCX6AIVEA4GB4B3NXFBLV4ET","short_pith_number":"pith:2QLCX6AI","canonical_record":{"source":{"id":"2207.02849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-05T14:01:15Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"3d40c66c225d94805abbfa6d0a98e7345f9a0c1a6266d63499e8b9ef026db14c","abstract_canon_sha256":"66196f8bc738150670da58a0e2e067bfb63dccf38f637163ce90f8ac348a771a"},"schema_version":"1.0"},"canonical_sha256":"d4162bf808a901c30781db6e50aebc24ece74b197a6683cb2482027564891080","source":{"kind":"arxiv","id":"2207.02849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.02849","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"2207.02849v2","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02849","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"2QLCX6AIVEA4","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_16","alias_value":"2QLCX6AIVEA4GB4B","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_8","alias_value":"2QLCX6AI","created_at":"2026-07-05T05:51:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:2QLCX6AIVEA4GB4B3NXFBLV4ET","target":"record","payload":{"canonical_record":{"source":{"id":"2207.02849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-05T14:01:15Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"3d40c66c225d94805abbfa6d0a98e7345f9a0c1a6266d63499e8b9ef026db14c","abstract_canon_sha256":"66196f8bc738150670da58a0e2e067bfb63dccf38f637163ce90f8ac348a771a"},"schema_version":"1.0"},"canonical_sha256":"d4162bf808a901c30781db6e50aebc24ece74b197a6683cb2482027564891080","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:26.202089Z","signature_b64":"IwgEbWJJvX4cbmBCxUFUmUirX5vbniKT254Ds2O0j9ZdkpI4zHP+dLCicK/K9DNg5rynDmrzLSNCtzj2c7pVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4162bf808a901c30781db6e50aebc24ece74b197a6683cb2482027564891080","last_reissued_at":"2026-07-05T05:51:26.201584Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:26.201584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.02849","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":"2026-07-05T05:51:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmyBjBMczCaI5m2JsXkUyr/xn+16/ce0kz3VrvStcTwVD4cqPn5qKClNV9iVmSMtFoFyXPEmtFxtMxaPRBk1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:07:52.705611Z"},"content_sha256":"9207b8210920c20c181346c0659c7f0a5694b0e49acd864e375236b6f2d87d2d","schema_version":"1.0","event_id":"sha256:9207b8210920c20c181346c0659c7f0a5694b0e49acd864e375236b6f2d87d2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:2QLCX6AIVEA4GB4B3NXFBLV4ET","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Betty: An Automatic Differentiation Library for Multilevel Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Eric Xing, Pengtao Xie, Sang Keun Choe, Willie Neiswanger","submitted_at":"2022-07-05T14:01:15Z","abstract_excerpt":"Gradient-based multilevel optimization (MLO) has gained attention as a framework for studying numerous problems, ranging from hyperparameter optimization and meta-learning to neural architecture search and reinforcement learning. However, gradients in MLO, which are obtained by composing best-response Jacobians via the chain rule, are notoriously difficult to implement and memory/compute intensive. We take an initial step towards closing this gap by introducing Betty, a software library for large-scale MLO. At its core, we devise a novel dataflow graph for MLO, which allows us to (1) develop e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02849","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.02849/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":"2026-07-05T05:51:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyzVZMPt7mPahgoP1bpkL8uXwSWT1GJNKCkPSDyTVzUzQzyoyoMu1bglKcihh3z+CPIfEgFF02W8fU/vvuedAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:07:52.706002Z"},"content_sha256":"2af149f6f2d1dbac6d3d2889620aecd1633c81c82fd37df0647efcfc9c15fa39","schema_version":"1.0","event_id":"sha256:2af149f6f2d1dbac6d3d2889620aecd1633c81c82fd37df0647efcfc9c15fa39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/bundle.json","state_url":"https://pith.science/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/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":"2026-08-17T16:07:52Z","links":{"resolver":"https://pith.science/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET","bundle":"https://pith.science/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/bundle.json","state":"https://pith.science/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QLCX6AIVEA4GB4B3NXFBLV4ET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2QLCX6AIVEA4GB4B3NXFBLV4ET","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":"66196f8bc738150670da58a0e2e067bfb63dccf38f637163ce90f8ac348a771a","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-05T14:01:15Z","title_canon_sha256":"3d40c66c225d94805abbfa6d0a98e7345f9a0c1a6266d63499e8b9ef026db14c"},"schema_version":"1.0","source":{"id":"2207.02849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.02849","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"2207.02849v2","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02849","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"2QLCX6AIVEA4","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_16","alias_value":"2QLCX6AIVEA4GB4B","created_at":"2026-07-05T05:51:26Z"},{"alias_kind":"pith_short_8","alias_value":"2QLCX6AI","created_at":"2026-07-05T05:51:26Z"}],"graph_snapshots":[{"event_id":"sha256:2af149f6f2d1dbac6d3d2889620aecd1633c81c82fd37df0647efcfc9c15fa39","target":"graph","created_at":"2026-07-05T05:51:26Z","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/2207.02849/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-based multilevel optimization (MLO) has gained attention as a framework for studying numerous problems, ranging from hyperparameter optimization and meta-learning to neural architecture search and reinforcement learning. However, gradients in MLO, which are obtained by composing best-response Jacobians via the chain rule, are notoriously difficult to implement and memory/compute intensive. We take an initial step towards closing this gap by introducing Betty, a software library for large-scale MLO. At its core, we devise a novel dataflow graph for MLO, which allows us to (1) develop e","authors_text":"Eric Xing, Pengtao Xie, Sang Keun Choe, Willie Neiswanger","cross_cats":["cs.AI","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-05T14:01:15Z","title":"Betty: An Automatic Differentiation Library for Multilevel Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02849","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":"sha256:9207b8210920c20c181346c0659c7f0a5694b0e49acd864e375236b6f2d87d2d","target":"record","created_at":"2026-07-05T05:51:26Z","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":"66196f8bc738150670da58a0e2e067bfb63dccf38f637163ce90f8ac348a771a","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-05T14:01:15Z","title_canon_sha256":"3d40c66c225d94805abbfa6d0a98e7345f9a0c1a6266d63499e8b9ef026db14c"},"schema_version":"1.0","source":{"id":"2207.02849","kind":"arxiv","version":2}},"canonical_sha256":"d4162bf808a901c30781db6e50aebc24ece74b197a6683cb2482027564891080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4162bf808a901c30781db6e50aebc24ece74b197a6683cb2482027564891080","first_computed_at":"2026-07-05T05:51:26.201584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:51:26.201584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IwgEbWJJvX4cbmBCxUFUmUirX5vbniKT254Ds2O0j9ZdkpI4zHP+dLCicK/K9DNg5rynDmrzLSNCtzj2c7pVCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:51:26.202089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.02849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9207b8210920c20c181346c0659c7f0a5694b0e49acd864e375236b6f2d87d2d","sha256:2af149f6f2d1dbac6d3d2889620aecd1633c81c82fd37df0647efcfc9c15fa39"],"state_sha256":"8a2926b8930a75cc99c7c61893438c2ba9a1cdd092f5d92ff4491e7476b3e451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0I3Hdj2N91M7kIwPWvF4gYEXChcdczLmgdro5e7iiVIAeQiQKifL8EmbJAoUe/UoS+Zbqk5jS7yjkr4VpPcAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:07:52.708815Z","bundle_sha256":"40ebc4a1c03661c2ad6d5f7e766639474d1a85a262c328e4f0def4af9b6b84d6"}}