{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XDZFECGUQLBDNWOXLOPXHGC427","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":"75d341cef8f7e05f3d6c80a946804858e004d7a870048298de03903212b2d918","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-16T07:56:54Z","title_canon_sha256":"5e8d14e3a5af1e678a43914fdf9fdbf1c7cb33d97e06f3664279715c8732ef4e"},"schema_version":"1.0","source":{"id":"2412.11521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11521","created_at":"2026-07-05T11:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11521v2","created_at":"2026-07-05T11:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11521","created_at":"2026-07-05T11:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"XDZFECGUQLBD","created_at":"2026-07-05T11:27:22Z"},{"alias_kind":"pith_short_16","alias_value":"XDZFECGUQLBDNWOX","created_at":"2026-07-05T11:27:22Z"},{"alias_kind":"pith_short_8","alias_value":"XDZFECGU","created_at":"2026-07-05T11:27:22Z"}],"graph_snapshots":[{"event_id":"sha256:d902dd88dccee9b14be25c96e71aabdda8082645f19e22afb53eca4e6be5c376","target":"graph","created_at":"2026-07-05T11:27:22Z","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/2412.11521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with standard architectures trained in a standard, supervised way -- learn symmetries from data. Inspired by real-world scenarios, we study a classification paradigm where data symmetries are only partially observed during training: some classes include all transformations of a cyclic group, while others -- only a subset. In the infinite-width limit, where kernel","authors_text":"Andrea Perin, Stephane Deny","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-16T07:56:54Z","title":"On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11521","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:b76079a755a89a852eec794157ea5cc63accfbbcfb5f99244160dcbe0bb63241","target":"record","created_at":"2026-07-05T11:27:22Z","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":"75d341cef8f7e05f3d6c80a946804858e004d7a870048298de03903212b2d918","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-16T07:56:54Z","title_canon_sha256":"5e8d14e3a5af1e678a43914fdf9fdbf1c7cb33d97e06f3664279715c8732ef4e"},"schema_version":"1.0","source":{"id":"2412.11521","kind":"arxiv","version":2}},"canonical_sha256":"b8f25208d482c236d9d75b9f73985cd7da67ce90f24de0630ebfaf9f9a91cadb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8f25208d482c236d9d75b9f73985cd7da67ce90f24de0630ebfaf9f9a91cadb","first_computed_at":"2026-07-05T11:27:22.730296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:22.730296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vyCzvCwofJXuWftbGv9SRvrh3IdRU13fiN5w04H/TJ9BLHM8VPozW0uiG24lLTZc46VJuS0oZMKWh0wQH75Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:22.730838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b76079a755a89a852eec794157ea5cc63accfbbcfb5f99244160dcbe0bb63241","sha256:d902dd88dccee9b14be25c96e71aabdda8082645f19e22afb53eca4e6be5c376"],"state_sha256":"d05ab6118327e8e39a3973682ede51a4bcde6e41781f8ca4bc388880ccefd4ca"}