{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JZX2HUFID5RZJ32XZJHRCUEGUY","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":"763977903d25d34f97a4385165f602f43f6c1547a3c7478fb75cbfcb939c9fc6","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-13T09:52:44Z","title_canon_sha256":"db017d029cc348e51202aa8fb441319856d06d725390ea65ac23c42142b48f65"},"schema_version":"1.0","source":{"id":"2406.08966","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.08966","created_at":"2026-06-05T01:15:11Z"},{"alias_kind":"arxiv_version","alias_value":"2406.08966v3","created_at":"2026-06-05T01:15:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.08966","created_at":"2026-06-05T01:15:11Z"},{"alias_kind":"pith_short_12","alias_value":"JZX2HUFID5RZ","created_at":"2026-06-05T01:15:11Z"},{"alias_kind":"pith_short_16","alias_value":"JZX2HUFID5RZJ32X","created_at":"2026-06-05T01:15:11Z"},{"alias_kind":"pith_short_8","alias_value":"JZX2HUFI","created_at":"2026-06-05T01:15:11Z"}],"graph_snapshots":[{"event_id":"sha256:1a08f320417d40629e8cb0e90f418060b1237a4da8fa8f549e6a6f7cb7adc0e5","target":"graph","created_at":"2026-06-05T01:15:11Z","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/2406.08966/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks. We first present a complete characterization of inputs indistinguishable by models derived by a given architecture. From this results, we derive how separability is influen","authors_text":"Bruno Lepri, Gabriele Santin, Marco Pacini, Xiaowen Dong","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-13T09:52:44Z","title":"Separation Power of Equivariant Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.08966","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":"sha256:2a7985bc3b54bed62de7f97315155d7be8a1c68c15fbf2b0dfc11af149937cc8","target":"record","created_at":"2026-06-05T01:15:11Z","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":"763977903d25d34f97a4385165f602f43f6c1547a3c7478fb75cbfcb939c9fc6","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-13T09:52:44Z","title_canon_sha256":"db017d029cc348e51202aa8fb441319856d06d725390ea65ac23c42142b48f65"},"schema_version":"1.0","source":{"id":"2406.08966","kind":"arxiv","version":3}},"canonical_sha256":"4e6fa3d0a81f6394ef57ca4f115086a611335d466f936acd049b8cd641643cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e6fa3d0a81f6394ef57ca4f115086a611335d466f936acd049b8cd641643cdf","first_computed_at":"2026-06-05T01:15:11.453295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:11.453295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rpw9m3pIhiczUwLMt/JtEav6IMDuquLZiSbl4yTvKtvxqa+OTOuREwupl6jw2KW0c2mGVnez3kF5BORWWsXRCA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:11.453784Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.08966","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a7985bc3b54bed62de7f97315155d7be8a1c68c15fbf2b0dfc11af149937cc8","sha256:1a08f320417d40629e8cb0e90f418060b1237a4da8fa8f549e6a6f7cb7adc0e5"],"state_sha256":"7bb9c90df1d4cea95aeaf22fe880d3a09b64d617f879593412e6920464ee0038"}