{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MDTOGS2T5YMZ7KAZLZXEJRREQT","short_pith_number":"pith:MDTOGS2T","canonical_record":{"source":{"id":"2405.15706","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T16:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"319b89895f2381444c46e2489ac412269f340bc95bc44ea1853895017396e71d","abstract_canon_sha256":"5079cda2dce644d05e5fb63ac24c07f49fd920c5dbe2367f67b2971fc94cdebf"},"schema_version":"1.0"},"canonical_sha256":"60e6e34b53ee199fa8195e6e44c62484c3fdf16d2f7746e4c5a0622282048289","source":{"kind":"arxiv","id":"2405.15706","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15706","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15706v3","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15706","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"MDTOGS2T5YMZ","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_16","alias_value":"MDTOGS2T5YMZ7KAZ","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_8","alias_value":"MDTOGS2T","created_at":"2026-07-05T09:50:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MDTOGS2T5YMZ7KAZLZXEJRREQT","target":"record","payload":{"canonical_record":{"source":{"id":"2405.15706","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T16:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"319b89895f2381444c46e2489ac412269f340bc95bc44ea1853895017396e71d","abstract_canon_sha256":"5079cda2dce644d05e5fb63ac24c07f49fd920c5dbe2367f67b2971fc94cdebf"},"schema_version":"1.0"},"canonical_sha256":"60e6e34b53ee199fa8195e6e44c62484c3fdf16d2f7746e4c5a0622282048289","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:50:47.648389Z","signature_b64":"28npFO8UCPlV0+cG9qChYo4xcgryNHOtkgXJ7rnsQv2GZ4La/kGgohSScGIbXfggVJoWgXOw06nKBu6Av75XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60e6e34b53ee199fa8195e6e44c62484c3fdf16d2f7746e4c5a0622282048289","last_reissued_at":"2026-07-05T09:50:47.647900Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:50:47.647900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.15706","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUkALY8kyepD6hhwAJOVW5uLtiDXNOvo3g+gw4dSni16IDn0LHrf8BDgRMrvrRBHGSNsfoN6HeFwuP6pcEudAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:52:48.805322Z"},"content_sha256":"c4bebbc8dfee433fa27579147dee3257ff0ff8885caa1bb30c41e6429bc35886","schema_version":"1.0","event_id":"sha256:c4bebbc8dfee433fa27579147dee3257ff0ff8885caa1bb30c41e6429bc35886"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MDTOGS2T5YMZ7KAZLZXEJRREQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Impact of Geometric Complexity on Neural Collapse in Transfer Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Benoit Dherin, Javier Gonzalvo, Michael Munn","submitted_at":"2024-05-24T16:52:09Z","abstract_excerpt":"Many of the recent remarkable advances in computer vision and language models can be attributed to the success of transfer learning via the pre-training of large foundation models. However, a theoretical framework which explains this empirical success is incomplete and remains an active area of research. Flatness of the loss surface and neural collapse have recently emerged as useful pre-training metrics which shed light on the implicit biases underlying pre-training. In this paper, we explore the geometric complexity of a model's learned representations as a fundamental mechanism that relates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15706","kind":"arxiv","version":3},"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/2405.15706/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":"2026-07-05T09:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJur+YbEqj+GcJlNSsI3jhHmyjB6wccAUhqFmjpzI4AWpz9NXZHPHxXTiOqOzxVIpO4LyOso9YKvoWMydeeSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:52:48.806239Z"},"content_sha256":"da936e7904b8ce802ba084e212dd9d57e2fdf874d88f416786d7c04eb83fdece","schema_version":"1.0","event_id":"sha256:da936e7904b8ce802ba084e212dd9d57e2fdf874d88f416786d7c04eb83fdece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/bundle.json","state_url":"https://pith.science/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/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":"2026-08-05T09:52:48Z","links":{"resolver":"https://pith.science/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT","bundle":"https://pith.science/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/bundle.json","state":"https://pith.science/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDTOGS2T5YMZ7KAZLZXEJRREQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MDTOGS2T5YMZ7KAZLZXEJRREQT","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":"5079cda2dce644d05e5fb63ac24c07f49fd920c5dbe2367f67b2971fc94cdebf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T16:52:09Z","title_canon_sha256":"319b89895f2381444c46e2489ac412269f340bc95bc44ea1853895017396e71d"},"schema_version":"1.0","source":{"id":"2405.15706","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15706","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15706v3","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15706","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"MDTOGS2T5YMZ","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_16","alias_value":"MDTOGS2T5YMZ7KAZ","created_at":"2026-07-05T09:50:47Z"},{"alias_kind":"pith_short_8","alias_value":"MDTOGS2T","created_at":"2026-07-05T09:50:47Z"}],"graph_snapshots":[{"event_id":"sha256:da936e7904b8ce802ba084e212dd9d57e2fdf874d88f416786d7c04eb83fdece","target":"graph","created_at":"2026-07-05T09:50:47Z","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/2405.15706/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many of the recent remarkable advances in computer vision and language models can be attributed to the success of transfer learning via the pre-training of large foundation models. However, a theoretical framework which explains this empirical success is incomplete and remains an active area of research. Flatness of the loss surface and neural collapse have recently emerged as useful pre-training metrics which shed light on the implicit biases underlying pre-training. In this paper, we explore the geometric complexity of a model's learned representations as a fundamental mechanism that relates","authors_text":"Benoit Dherin, Javier Gonzalvo, Michael Munn","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T16:52:09Z","title":"The Impact of Geometric Complexity on Neural Collapse in Transfer Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15706","kind":"arxiv","version":3},"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:c4bebbc8dfee433fa27579147dee3257ff0ff8885caa1bb30c41e6429bc35886","target":"record","created_at":"2026-07-05T09:50:47Z","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":"5079cda2dce644d05e5fb63ac24c07f49fd920c5dbe2367f67b2971fc94cdebf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T16:52:09Z","title_canon_sha256":"319b89895f2381444c46e2489ac412269f340bc95bc44ea1853895017396e71d"},"schema_version":"1.0","source":{"id":"2405.15706","kind":"arxiv","version":3}},"canonical_sha256":"60e6e34b53ee199fa8195e6e44c62484c3fdf16d2f7746e4c5a0622282048289","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60e6e34b53ee199fa8195e6e44c62484c3fdf16d2f7746e4c5a0622282048289","first_computed_at":"2026-07-05T09:50:47.647900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:47.647900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28npFO8UCPlV0+cG9qChYo4xcgryNHOtkgXJ7rnsQv2GZ4La/kGgohSScGIbXfggVJoWgXOw06nKBu6Av75XBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:47.648389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.15706","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4bebbc8dfee433fa27579147dee3257ff0ff8885caa1bb30c41e6429bc35886","sha256:da936e7904b8ce802ba084e212dd9d57e2fdf874d88f416786d7c04eb83fdece"],"state_sha256":"41012688624642fd889776f299ede6f36adc27409964cf3ca39d4a224cedf69c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2QTsmTXZoU5XoAPSXfAw4SoGKdVv2NLzo2VK/P14hkxzPrLmDpxGgY2vaGYwyJ4k6JEq42B8UtAWs+/p+MVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T09:52:48.811364Z","bundle_sha256":"25d75541bdad3667b0d03f0776205315467f83c8af4389b0c0b0db776947bfa1"}}