{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:P5KXMFVBBNTR6XCXQAXYQUM3RW","short_pith_number":"pith:P5KXMFVB","canonical_record":{"source":{"id":"2106.02793","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-05T04:37:03Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0fb872dcb6c9752f38b79d347f0f62d906fd555c82e1b0dea1356e215103ae2f","abstract_canon_sha256":"857d5a2ad07a2996eef8caff1bfe552264557e259a829dbbbc98ec6e8526cda6"},"schema_version":"1.0"},"canonical_sha256":"7f557616a10b671f5c57802f88519b8d9a23a41e915da79a4b5ed97564ccbc39","source":{"kind":"arxiv","id":"2106.02793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.02793","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2106.02793v1","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.02793","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"P5KXMFVBBNTR","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"P5KXMFVBBNTR6XCX","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"P5KXMFVB","created_at":"2026-07-05T02:46:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:P5KXMFVBBNTR6XCXQAXYQUM3RW","target":"record","payload":{"canonical_record":{"source":{"id":"2106.02793","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-05T04:37:03Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0fb872dcb6c9752f38b79d347f0f62d906fd555c82e1b0dea1356e215103ae2f","abstract_canon_sha256":"857d5a2ad07a2996eef8caff1bfe552264557e259a829dbbbc98ec6e8526cda6"},"schema_version":"1.0"},"canonical_sha256":"7f557616a10b671f5c57802f88519b8d9a23a41e915da79a4b5ed97564ccbc39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:30.067529Z","signature_b64":"9ZJU4LzM0vu8brcPQlrNu7T0TxSqYIouri6IrHSnqAgA49e8Agljc/ah53XSsnfYZag3rjZvvI527iyxKxwkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f557616a10b671f5c57802f88519b8d9a23a41e915da79a4b5ed97564ccbc39","last_reissued_at":"2026-07-05T02:46:30.066994Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:30.066994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.02793","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":"2026-07-05T02:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+xCADR3sicUYtovSRprqn6vAYfJlIefQGoTQKPVh/2/UyHYZimPy8CQObWlOemZMg/0iX93ApYXfSjuFxgzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:44:50.394077Z"},"content_sha256":"6772cb4042c3e2f5161ae912dbca113bb7fcb304723e241b68f9c7d2e7c95e72","schema_version":"1.0","event_id":"sha256:6772cb4042c3e2f5161ae912dbca113bb7fcb304723e241b68f9c7d2e7c95e72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:P5KXMFVBBNTR6XCXQAXYQUM3RW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving hybrid machine learning tasks by traversing weight space geodesics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Guruprasad Raghavan, Matt Thomson","submitted_at":"2021-06-05T04:37:03Z","abstract_excerpt":"Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given machine learning problem. Therefore, geometric concepts can be applied to analyze and understand theoretical properties of machine learning strategies as well as to develop new algorithms. In this paper, we address three seemingly unrelated open questions in machine learning by viewing them through a unified framework grounded in differential geometry. Spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.02793/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":"2026-07-05T02:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RB7WRMBHFVSNY0mqwEmCcTrTKGGjcTpQGpz5uLSwe4utjIUDH51RuE6aUktYq4owOQ9YtAZBhMmlZ2NWlaIpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:44:50.394596Z"},"content_sha256":"b2abac803e44855bd8aec723528e1d35db6db1bbd790c0a525305502b10f0e59","schema_version":"1.0","event_id":"sha256:b2abac803e44855bd8aec723528e1d35db6db1bbd790c0a525305502b10f0e59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/bundle.json","state_url":"https://pith.science/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/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":"2026-08-07T08:44:50Z","links":{"resolver":"https://pith.science/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW","bundle":"https://pith.science/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/bundle.json","state":"https://pith.science/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5KXMFVBBNTR6XCXQAXYQUM3RW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:P5KXMFVBBNTR6XCXQAXYQUM3RW","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":"857d5a2ad07a2996eef8caff1bfe552264557e259a829dbbbc98ec6e8526cda6","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-05T04:37:03Z","title_canon_sha256":"0fb872dcb6c9752f38b79d347f0f62d906fd555c82e1b0dea1356e215103ae2f"},"schema_version":"1.0","source":{"id":"2106.02793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.02793","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2106.02793v1","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.02793","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"P5KXMFVBBNTR","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"P5KXMFVBBNTR6XCX","created_at":"2026-07-05T02:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"P5KXMFVB","created_at":"2026-07-05T02:46:30Z"}],"graph_snapshots":[{"event_id":"sha256:b2abac803e44855bd8aec723528e1d35db6db1bbd790c0a525305502b10f0e59","target":"graph","created_at":"2026-07-05T02:46:30Z","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/2106.02793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given machine learning problem. Therefore, geometric concepts can be applied to analyze and understand theoretical properties of machine learning strategies as well as to develop new algorithms. In this paper, we address three seemingly unrelated open questions in machine learning by viewing them through a unified framework grounded in differential geometry. Spec","authors_text":"Guruprasad Raghavan, Matt Thomson","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-05T04:37:03Z","title":"Solving hybrid machine learning tasks by traversing weight space geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02793","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":"sha256:6772cb4042c3e2f5161ae912dbca113bb7fcb304723e241b68f9c7d2e7c95e72","target":"record","created_at":"2026-07-05T02:46:30Z","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":"857d5a2ad07a2996eef8caff1bfe552264557e259a829dbbbc98ec6e8526cda6","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-05T04:37:03Z","title_canon_sha256":"0fb872dcb6c9752f38b79d347f0f62d906fd555c82e1b0dea1356e215103ae2f"},"schema_version":"1.0","source":{"id":"2106.02793","kind":"arxiv","version":1}},"canonical_sha256":"7f557616a10b671f5c57802f88519b8d9a23a41e915da79a4b5ed97564ccbc39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f557616a10b671f5c57802f88519b8d9a23a41e915da79a4b5ed97564ccbc39","first_computed_at":"2026-07-05T02:46:30.066994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:46:30.066994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ZJU4LzM0vu8brcPQlrNu7T0TxSqYIouri6IrHSnqAgA49e8Agljc/ah53XSsnfYZag3rjZvvI527iyxKxwkBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:46:30.067529Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.02793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6772cb4042c3e2f5161ae912dbca113bb7fcb304723e241b68f9c7d2e7c95e72","sha256:b2abac803e44855bd8aec723528e1d35db6db1bbd790c0a525305502b10f0e59"],"state_sha256":"1d641a4a88f1adc5a71882ff81a339c5c8c2b41996cac73929fe3dab985d08e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnE9kuso1kr+D2BS042pnIrvJQ0pp7fQCAaOT3TL0liLzlI30VeBZG9WPFyfY9gfHoxZWwryIm+pjrM0FcVCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T08:44:50.421899Z","bundle_sha256":"e7bf2d97fbbbf26a9227314c50cbed2370808f27e33b3de1287fe2595c09a833"}}