{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PDOMEN5HHJYFKQQUSDW22DKQ6I","short_pith_number":"pith:PDOMEN5H","canonical_record":{"source":{"id":"1803.01273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-04T00:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"4ba5887ed583021e6c7fdb83dedcbb814d45a7253be4951fdad7380367b0b899","abstract_canon_sha256":"a5197b27fa8105dfdee27fba78bed1bbb92e7d803d14df93e5bd459b1d0a798f"},"schema_version":"1.0"},"canonical_sha256":"78dcc237a73a7055421490edad0d50f23f730577ad2c16b4ecb171c006141c2f","source":{"kind":"arxiv","id":"1803.01273","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01273","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01273v2","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01273","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"PDOMEN5HHJYF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDOMEN5HHJYFKQQU","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDOMEN5H","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PDOMEN5HHJYFKQQUSDW22DKQ6I","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-04T00:25:09Z","cross_cats_sorted":[],"title_canon_sha256":"4ba5887ed583021e6c7fdb83dedcbb814d45a7253be4951fdad7380367b0b899","abstract_canon_sha256":"a5197b27fa8105dfdee27fba78bed1bbb92e7d803d14df93e5bd459b1d0a798f"},"schema_version":"1.0"},"canonical_sha256":"78dcc237a73a7055421490edad0d50f23f730577ad2c16b4ecb171c006141c2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:54.952764Z","signature_b64":"xbMXjhx4fMREteTh/LUZPYR3FmdlPcy5DxWzNadkQHt7tHjBFQJwLyUn8SZmgWTj6vlvJXNVukrTpMnT167SCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78dcc237a73a7055421490edad0d50f23f730577ad2c16b4ecb171c006141c2f","last_reissued_at":"2026-05-18T00:13:54.951839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:54.951839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01273","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":"2026-05-18T00:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Onq7/BrLPU63M3xZj6687PkNuMb2/FZc0yNdRZ7gTNctYfQkqmTxrUYnWgd9LtKdEqOKED3rszOJuFG1wDgeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:45:04.375784Z"},"content_sha256":"7e327dac3dc52b21cf817dc17d304b5eeaf9e9c685ac95db0f35c1ea73763165","schema_version":"1.0","event_id":"sha256:7e327dac3dc52b21cf817dc17d304b5eeaf9e9c685ac95db0f35c1ea73763165"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PDOMEN5HHJYFKQQUSDW22DKQ6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accelerating Natural Gradient with Higher-Order Invariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jiaming Song, Stefano Ermon, Yang Song","submitted_at":"2018-03-04T00:25:09Z","abstract_excerpt":"An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with small but finite step sizes. In this paper, we study invariance properties from a combined perspective of Riemannian geometry and numerical differential equation solving. We define the order of invariance of a numerical method to be its convergence order to an invariant solution. We propose to use higher-order integrators and geodesic corrections to obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01273","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":"2026-05-18T00:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBpE6gtMFJsQ2ScKaM1Z0xeMyENrkiMPzw9WTSF9bvhP0xJd6f+wquPQrkvXj8A1fvF0l8tAoGuIepHbNJPbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:45:04.376407Z"},"content_sha256":"3c2e50636817793c5d6c964978086beb0b41e5bb6ee2b1c48088102b767b2a12","schema_version":"1.0","event_id":"sha256:3c2e50636817793c5d6c964978086beb0b41e5bb6ee2b1c48088102b767b2a12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/bundle.json","state_url":"https://pith.science/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/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":"2026-06-07T06:45:04Z","links":{"resolver":"https://pith.science/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I","bundle":"https://pith.science/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/bundle.json","state":"https://pith.science/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDOMEN5HHJYFKQQUSDW22DKQ6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PDOMEN5HHJYFKQQUSDW22DKQ6I","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":"a5197b27fa8105dfdee27fba78bed1bbb92e7d803d14df93e5bd459b1d0a798f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-04T00:25:09Z","title_canon_sha256":"4ba5887ed583021e6c7fdb83dedcbb814d45a7253be4951fdad7380367b0b899"},"schema_version":"1.0","source":{"id":"1803.01273","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01273","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01273v2","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01273","created_at":"2026-05-18T00:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"PDOMEN5HHJYF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDOMEN5HHJYFKQQU","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDOMEN5H","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:3c2e50636817793c5d6c964978086beb0b41e5bb6ee2b1c48088102b767b2a12","target":"graph","created_at":"2026-05-18T00:13:54Z","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":"An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with small but finite step sizes. In this paper, we study invariance properties from a combined perspective of Riemannian geometry and numerical differential equation solving. We define the order of invariance of a numerical method to be its convergence order to an invariant solution. We propose to use higher-order integrators and geodesic corrections to obtain ","authors_text":"Jiaming Song, Stefano Ermon, Yang Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-04T00:25:09Z","title":"Accelerating Natural Gradient with Higher-Order Invariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01273","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":"sha256:7e327dac3dc52b21cf817dc17d304b5eeaf9e9c685ac95db0f35c1ea73763165","target":"record","created_at":"2026-05-18T00:13:54Z","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":"a5197b27fa8105dfdee27fba78bed1bbb92e7d803d14df93e5bd459b1d0a798f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-04T00:25:09Z","title_canon_sha256":"4ba5887ed583021e6c7fdb83dedcbb814d45a7253be4951fdad7380367b0b899"},"schema_version":"1.0","source":{"id":"1803.01273","kind":"arxiv","version":2}},"canonical_sha256":"78dcc237a73a7055421490edad0d50f23f730577ad2c16b4ecb171c006141c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78dcc237a73a7055421490edad0d50f23f730577ad2c16b4ecb171c006141c2f","first_computed_at":"2026-05-18T00:13:54.951839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:54.951839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbMXjhx4fMREteTh/LUZPYR3FmdlPcy5DxWzNadkQHt7tHjBFQJwLyUn8SZmgWTj6vlvJXNVukrTpMnT167SCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:54.952764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01273","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e327dac3dc52b21cf817dc17d304b5eeaf9e9c685ac95db0f35c1ea73763165","sha256:3c2e50636817793c5d6c964978086beb0b41e5bb6ee2b1c48088102b767b2a12"],"state_sha256":"f8599857f2c5e1b39f781dcab0f9e132c409d8d8f6bc18a07aa7d7803f7224a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhlMU5UEvHX0YcR9b4wBYp9waNmz0drGHYgZiKrL7BnHZrkN+v8Mrzfwq8nauf51LnB8+ALcwFd19OblSVJ9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:45:04.379441Z","bundle_sha256":"c217498392e1f2237073ca187770f28a52dbbf05c0ac0b1356f8227b61a1c149"}}