{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CFWW5RFZZSYEH5XRHTZRCZKYGS","short_pith_number":"pith:CFWW5RFZ","schema_version":"1.0","canonical_sha256":"116d6ec4b9ccb043f6f13cf31165583480f61e1618ac0abb27af136580563482","source":{"kind":"arxiv","id":"2606.30822","version":1},"attestation_state":"computed","paper":{"title":"Separation Capacity of Scattering Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.CV","math.IT"],"primary_cat":"stat.ML","authors_text":"Helmut B\\\"olcskei, Konstantin H\\\"aberle","submitted_at":"2026-06-29T18:51:44Z","abstract_excerpt":"In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity derived from counting the number of realizable dichotomies (i.e., binary label assignments). Our contributions are threefold. First, we extend Cover's framework by establishing a conceptually insightful and practically useful formulation for the separation capacity. Second, leveragi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.30822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-06-29T18:51:44Z","cross_cats_sorted":["cs.IT","cs.LG","math.CV","math.IT"],"title_canon_sha256":"a250eaabe2a6ab37950be3706c5fe3a0ccc24b7b8cce4adf5fd9e473165eb313","abstract_canon_sha256":"09340e1547c1cb5178b2e2f13a5ab427fabe58c31dec5e42d60447133274a655"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T00:17:18.483748Z","signature_b64":"MLgarLIOMOILa/u+rANFeyURGitJMbcrnEXx3fJew42rxO8KsLRJ9WjCAJaRHAS5fJ4kAnf7I0dGdad9jYDDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"116d6ec4b9ccb043f6f13cf31165583480f61e1618ac0abb27af136580563482","last_reissued_at":"2026-07-01T00:17:18.483335Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T00:17:18.483335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separation Capacity of Scattering Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.CV","math.IT"],"primary_cat":"stat.ML","authors_text":"Helmut B\\\"olcskei, Konstantin H\\\"aberle","submitted_at":"2026-06-29T18:51:44Z","abstract_excerpt":"In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity derived from counting the number of realizable dichotomies (i.e., binary label assignments). Our contributions are threefold. First, we extend Cover's framework by establishing a conceptually insightful and practically useful formulation for the separation capacity. Second, leveragi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30822","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/2606.30822/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.30822","created_at":"2026-07-01T00:17:18.483402+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30822v1","created_at":"2026-07-01T00:17:18.483402+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30822","created_at":"2026-07-01T00:17:18.483402+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFWW5RFZZSYE","created_at":"2026-07-01T00:17:18.483402+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFWW5RFZZSYEH5XR","created_at":"2026-07-01T00:17:18.483402+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFWW5RFZ","created_at":"2026-07-01T00:17:18.483402+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.01010","citing_title":"Function-Counting Theory for Low-Dimensional Data Structures","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS","json":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS.json","graph_json":"https://pith.science/api/pith-number/CFWW5RFZZSYEH5XRHTZRCZKYGS/graph.json","events_json":"https://pith.science/api/pith-number/CFWW5RFZZSYEH5XRHTZRCZKYGS/events.json","paper":"https://pith.science/paper/CFWW5RFZ"},"agent_actions":{"view_html":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS","download_json":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS.json","view_paper":"https://pith.science/paper/CFWW5RFZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30822&json=true","fetch_graph":"https://pith.science/api/pith-number/CFWW5RFZZSYEH5XRHTZRCZKYGS/graph.json","fetch_events":"https://pith.science/api/pith-number/CFWW5RFZZSYEH5XRHTZRCZKYGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS/action/storage_attestation","attest_author":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS/action/author_attestation","sign_citation":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS/action/citation_signature","submit_replication":"https://pith.science/pith/CFWW5RFZZSYEH5XRHTZRCZKYGS/action/replication_record"}},"created_at":"2026-07-01T00:17:18.483402+00:00","updated_at":"2026-07-01T00:17:18.483402+00:00"}