{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5XQ6V2244NW6VKE634ATDAWZ7L","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":"0a202ec330836c4c2500e5623f246c153a490778bde297b3f77380818356c3ec","cross_cats_sorted":["cond-mat.dis-nn","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T14:44:06Z","title_canon_sha256":"4522539b8b8c3d792457f87e5005f4e663fe5b819c64d6bd728398a35ea9efd4"},"schema_version":"1.0","source":{"id":"2605.13612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13612","created_at":"2026-05-18T02:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13612v1","created_at":"2026-05-18T02:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13612","created_at":"2026-05-18T02:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"5XQ6V2244NW6","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"5XQ6V2244NW6VKE6","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"5XQ6V224","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:d3d4c32959e45cfc77afbc223a4e6cc8260196577bffbb5e84c941dff1c2ef5a","target":"graph","created_at":"2026-05-18T02:44:18Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity, and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that, in the stylized limit of gradient-based training, the dynamics at each layer decouple so that the next layer can independently select directions with maximal accessible low-degree correlation to the label."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Neural Low-Degree Filtering models deep learning as an explicit iterative spectral process in which each layer selects features by maximal low-degree correlation to the label."}],"snapshot_sha256":"98eee99d1edb500da12c14d05e1dfb95a62ef266eef7b6320f1955424f3909fb"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a n","authors_text":"Florent Krzakala, Hugo Tabanelli, Luca Arnaboldi, Matteo Vilucchio, Yatin Dandi","cross_cats":["cond-mat.dis-nn","stat.ML"],"headline":"Neural Low-Degree Filtering models deep learning as an explicit iterative spectral process in which each layer selects features by maximal low-degree correlation to the label.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T14:44:06Z","title":"Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning"},"references":{"count":123,"internal_anchors":1,"resolved_work":123,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Deep learning.nature, 521(7553):436–444, 2015","work_id":"8c42ff53-c495-4b0d-8fa1-03b2d8f9af31","year":2015},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"The unreasonable effectiveness of deep learning in artificial intelligence","work_id":"36377418-d23c-43fe-973c-011bd3d00571","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Visualizing and understanding convolutional networks","work_id":"60453a30-3d6f-49ac-a8e6-80fb37b14549","year":2014},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"How transferable are features in deep neural networks?Advances in neural information processing systems, 27","work_id":"827b6bdf-60c2-460c-bcc4-a153256c22ad","year":2014},{"cited_arxiv_id":"2405.07987","doi":"","is_internal_anchor":false,"ref_index":5,"title":"The Platonic Representation Hypothesis","work_id":"950baa06-36a7-4010-a959-7304fb1ce08b","year":2024}],"snapshot_sha256":"47144f6f9da2afba6d4424581cdb272f38fae383f0e6efd7a4ea4e2735efa856"},"source":{"id":"2605.13612","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T19:35:40.881672Z","id":"da530274-bb01-41b7-a323-694891d498b7","model_set":{"reader":"grok-4.3"},"one_line_summary":"Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Neural Low-Degree Filtering models deep learning as an explicit iterative spectral process in which each layer selects features by maximal low-degree correlation to the label.","strongest_claim":"Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity, and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality.","weakest_assumption":"The assumption that, in the stylized limit of gradient-based training, the dynamics at each layer decouple so that the next layer can independently select directions with maximal accessible low-degree correlation to the label."}},"verdict_id":"da530274-bb01-41b7-a323-694891d498b7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:34952cb222b10cd6a1a3a992b8ccdb48e8f2b9dc106d147a4f9324ea4b0b8b13","target":"record","created_at":"2026-05-18T02:44:18Z","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":"0a202ec330836c4c2500e5623f246c153a490778bde297b3f77380818356c3ec","cross_cats_sorted":["cond-mat.dis-nn","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-13T14:44:06Z","title_canon_sha256":"4522539b8b8c3d792457f87e5005f4e663fe5b819c64d6bd728398a35ea9efd4"},"schema_version":"1.0","source":{"id":"2605.13612","kind":"arxiv","version":1}},"canonical_sha256":"ede1eaeb5ce36deaa89edf013182d9fad6af9d0895d3d9535f83eb945b919f32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ede1eaeb5ce36deaa89edf013182d9fad6af9d0895d3d9535f83eb945b919f32","first_computed_at":"2026-05-18T02:44:18.035589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:18.035589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WRFZNFLQP3hGtTQGloQ5PmmBvOAZZ7oqEodLwJppI5fUVe9Wb7cJMQh0hxLoG4HLcR2WOcZ3Uo+qSd1lxhicDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:18.036062Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34952cb222b10cd6a1a3a992b8ccdb48e8f2b9dc106d147a4f9324ea4b0b8b13","sha256:d3d4c32959e45cfc77afbc223a4e6cc8260196577bffbb5e84c941dff1c2ef5a"],"state_sha256":"63a494c7e7aa64d7c0c029a24dd80a7ed5fad7307034c7081a2d503386968c21"}