{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GG2LXSX3HM457XF3NQMULA62YO","short_pith_number":"pith:GG2LXSX3","schema_version":"1.0","canonical_sha256":"31b4bbcafb3b39dfdcbb6c194583dac3bb03d661e23629730abd50c841b14278","source":{"kind":"arxiv","id":"2606.10324","version":1},"attestation_state":"computed","paper":{"title":"Rank Collapse, Fixed Points, and the Renormalization Group Structure of MLP Residual Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","stat.ML"],"primary_cat":"cs.LG","authors_text":"Irina Rish, Parviz Haggi-Mani","submitted_at":"2026-06-09T02:19:26Z","abstract_excerpt":"The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure "},"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":"2606.10324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T02:19:26Z","cross_cats_sorted":["cond-mat.stat-mech","stat.ML"],"title_canon_sha256":"d500d450cfcba34949312cd84be918f2da079c91360c1a6a499a8394d8f0051c","abstract_canon_sha256":"1c933b65848ccaeac1d5b0f44ec7996b69968dee140faed0487a5808fbd1f1b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:11.936536Z","signature_b64":"24z1+dJj2RtSqwjknxhixh26IU59tbhRI5B/TgULgAoyqzb4Bid6BqdmIB7GXDn28fzaxG482y8rUwR+7qzbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31b4bbcafb3b39dfdcbb6c194583dac3bb03d661e23629730abd50c841b14278","last_reissued_at":"2026-06-10T01:10:11.935677Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:11.935677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank Collapse, Fixed Points, and the Renormalization Group Structure of MLP Residual Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","stat.ML"],"primary_cat":"cs.LG","authors_text":"Irina Rish, Parviz Haggi-Mani","submitted_at":"2026-06-09T02:19:26Z","abstract_excerpt":"The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10324","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/2606.10324/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":"2606.10324","created_at":"2026-06-10T01:10:11.935826+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10324v1","created_at":"2026-06-10T01:10:11.935826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10324","created_at":"2026-06-10T01:10:11.935826+00:00"},{"alias_kind":"pith_short_12","alias_value":"GG2LXSX3HM45","created_at":"2026-06-10T01:10:11.935826+00:00"},{"alias_kind":"pith_short_16","alias_value":"GG2LXSX3HM457XF3","created_at":"2026-06-10T01:10:11.935826+00:00"},{"alias_kind":"pith_short_8","alias_value":"GG2LXSX3","created_at":"2026-06-10T01:10:11.935826+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO","json":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO.json","graph_json":"https://pith.science/api/pith-number/GG2LXSX3HM457XF3NQMULA62YO/graph.json","events_json":"https://pith.science/api/pith-number/GG2LXSX3HM457XF3NQMULA62YO/events.json","paper":"https://pith.science/paper/GG2LXSX3"},"agent_actions":{"view_html":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO","download_json":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO.json","view_paper":"https://pith.science/paper/GG2LXSX3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10324&json=true","fetch_graph":"https://pith.science/api/pith-number/GG2LXSX3HM457XF3NQMULA62YO/graph.json","fetch_events":"https://pith.science/api/pith-number/GG2LXSX3HM457XF3NQMULA62YO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO/action/storage_attestation","attest_author":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO/action/author_attestation","sign_citation":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO/action/citation_signature","submit_replication":"https://pith.science/pith/GG2LXSX3HM457XF3NQMULA62YO/action/replication_record"}},"created_at":"2026-06-10T01:10:11.935826+00:00","updated_at":"2026-06-10T01:10:11.935826+00:00"}