{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VQNV6DE5RBZ7TVTMBVVDDO26IZ","short_pith_number":"pith:VQNV6DE5","canonical_record":{"source":{"id":"2007.04504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-09T01:39:34Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f11ad7f111de41c393992b13b194909168095dca877c88f161e1042979408818","abstract_canon_sha256":"8ed86c77a20f1482c235801c17b05f4a1dabcd5db6ce9d5dc657364b4934c0ce"},"schema_version":"1.0"},"canonical_sha256":"ac1b5f0c9d8873f9d66c0d6a31bb5e4640fe5916f7a616e4ed0e359a3c5b40ec","source":{"kind":"arxiv","id":"2007.04504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.04504","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.04504v2","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.04504","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"VQNV6DE5RBZ7","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_16","alias_value":"VQNV6DE5RBZ7TVTM","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_8","alias_value":"VQNV6DE5","created_at":"2026-07-05T01:45:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VQNV6DE5RBZ7TVTMBVVDDO26IZ","target":"record","payload":{"canonical_record":{"source":{"id":"2007.04504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-09T01:39:34Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"f11ad7f111de41c393992b13b194909168095dca877c88f161e1042979408818","abstract_canon_sha256":"8ed86c77a20f1482c235801c17b05f4a1dabcd5db6ce9d5dc657364b4934c0ce"},"schema_version":"1.0"},"canonical_sha256":"ac1b5f0c9d8873f9d66c0d6a31bb5e4640fe5916f7a616e4ed0e359a3c5b40ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:45:29.192478Z","signature_b64":"WFYvicxRYGVga0Ed3RUPRG+ZOaUmnu0XZekfBFeEmYAWZuGim6VJf2AWuLx3XxFrjtSzMHKnk1rqPhisjfg2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac1b5f0c9d8873f9d66c0d6a31bb5e4640fe5916f7a616e4ed0e359a3c5b40ec","last_reissued_at":"2026-07-05T01:45:29.192069Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:45:29.192069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.04504","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":"2026-07-05T01:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cOwk0Q6rozbWs84QmGBn1XJW00U4T8NGHspCDk371CzhgemZFRaEQ1qUYFpM9NaCXoIpFvtCg3DtKS9ub3gsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:38:13.524488Z"},"content_sha256":"77fff391f75bcd179a98ea5ba95b8c5124e1b74c45b9bbaa7bab6876ecf99682","schema_version":"1.0","event_id":"sha256:77fff391f75bcd179a98ea5ba95b8c5124e1b74c45b9bbaa7bab6876ecf99682"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VQNV6DE5RBZ7TVTMBVVDDO26IZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Differential Equations that are Easy to Solve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"David Duvenaud, Jacob Kelly, Jesse Bettencourt, Matthew James Johnson","submitted_at":"2020-07-09T01:39:34Z","abstract_excerpt":"Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04504","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/2007.04504/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":"2026-07-05T01:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlTl4S4Hs6ECLJLLCR0EDdxgeyTNCculQasb79vt8AbO83yQukBBdyx3IhvY+zOymcbLaBZYzGR0E+fPyJQYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:38:13.525201Z"},"content_sha256":"627f670db1185bf0b777fdcc40ea4f6abaa2051b77a29a9a8160aced4b4b1a71","schema_version":"1.0","event_id":"sha256:627f670db1185bf0b777fdcc40ea4f6abaa2051b77a29a9a8160aced4b4b1a71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/bundle.json","state_url":"https://pith.science/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/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":"2026-08-13T18:38:13Z","links":{"resolver":"https://pith.science/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ","bundle":"https://pith.science/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/bundle.json","state":"https://pith.science/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQNV6DE5RBZ7TVTMBVVDDO26IZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VQNV6DE5RBZ7TVTMBVVDDO26IZ","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":"8ed86c77a20f1482c235801c17b05f4a1dabcd5db6ce9d5dc657364b4934c0ce","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-09T01:39:34Z","title_canon_sha256":"f11ad7f111de41c393992b13b194909168095dca877c88f161e1042979408818"},"schema_version":"1.0","source":{"id":"2007.04504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.04504","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.04504v2","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.04504","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"VQNV6DE5RBZ7","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_16","alias_value":"VQNV6DE5RBZ7TVTM","created_at":"2026-07-05T01:45:29Z"},{"alias_kind":"pith_short_8","alias_value":"VQNV6DE5","created_at":"2026-07-05T01:45:29Z"}],"graph_snapshots":[{"event_id":"sha256:627f670db1185bf0b777fdcc40ea4f6abaa2051b77a29a9a8160aced4b4b1a71","target":"graph","created_at":"2026-07-05T01:45:29Z","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/2007.04504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training su","authors_text":"David Duvenaud, Jacob Kelly, Jesse Bettencourt, Matthew James Johnson","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-09T01:39:34Z","title":"Learning Differential Equations that are Easy to Solve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04504","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":"sha256:77fff391f75bcd179a98ea5ba95b8c5124e1b74c45b9bbaa7bab6876ecf99682","target":"record","created_at":"2026-07-05T01:45:29Z","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":"8ed86c77a20f1482c235801c17b05f4a1dabcd5db6ce9d5dc657364b4934c0ce","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-07-09T01:39:34Z","title_canon_sha256":"f11ad7f111de41c393992b13b194909168095dca877c88f161e1042979408818"},"schema_version":"1.0","source":{"id":"2007.04504","kind":"arxiv","version":2}},"canonical_sha256":"ac1b5f0c9d8873f9d66c0d6a31bb5e4640fe5916f7a616e4ed0e359a3c5b40ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac1b5f0c9d8873f9d66c0d6a31bb5e4640fe5916f7a616e4ed0e359a3c5b40ec","first_computed_at":"2026-07-05T01:45:29.192069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:29.192069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFYvicxRYGVga0Ed3RUPRG+ZOaUmnu0XZekfBFeEmYAWZuGim6VJf2AWuLx3XxFrjtSzMHKnk1rqPhisjfg2BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:29.192478Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.04504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77fff391f75bcd179a98ea5ba95b8c5124e1b74c45b9bbaa7bab6876ecf99682","sha256:627f670db1185bf0b777fdcc40ea4f6abaa2051b77a29a9a8160aced4b4b1a71"],"state_sha256":"de9a2f668d867eac0fdaea66af59e850425509f0946161b9f1efa0c9a151a33a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qkOSrpohDH679vp73UJQ+LnMNPYDj7eJmXUHO+f1+XDw8mwJnNHAPN+3GweTIFNES70GVfoTVbUzDaPP0sPOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:38:13.536589Z","bundle_sha256":"7707c980f0f8067b6285ec165f584c825c7c97435a6d9913d49bf19fcfe4e43a"}}