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However, common Neural Sheaf Diffusion implementations rely on SVD-based sheaf normalization and dense per-edge restriction maps, which scale with stalk dimension, require frequent Laplacian rebuilds, and yield brittle gradients. To address these limitations, we introduce Polynomial Neural Sheaf Diffusion (PolyNSD), a new sheaf diffusion approach whose propagation operator is a degree-K polynomial in a normalised sheaf Laplacian, evaluated via a stable three-term recurrence on a spectrally rescaled operator. This provides an explicit K-hop receptive field in a single layer (independently of the stalk dimension), with a trainable spectral res","title":"Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves","url":"https://arxiv.org/abs/2512.00242","vendor":"arxiv_cs_ai"},"summary":"arXiv:2512.00242v3 Announce Type: replace-cross \nAbstract: Sheaf Neural Networks equip graph structures with a cellular sheaf: a geometric structure which assigns local vector spaces (stalks) and a linear learnable restriction/transport maps to nodes and edges, yielding an edge-aware inductive bias that handles heterophily and limits oversmoothing. However, common Neural Sheaf Diffusion implementations rely on SVD-based sheaf normalization and dense per-edge restriction maps, which scale with stalk dimension, require frequent Laplacian rebuilds, and yield brittle gradients. To address these limitations, we introduce Polynomial Neural Sheaf Diffusion (PolyNSD), a new sheaf diffusion approach whose propagation operator is a degree-K polynomial in a normalised sheaf Laplacian, evaluated via a stable three-term recurrence on a spectrally rescaled operator. This provides an explicit K-hop receptive field in a single layer (independently of the stalk dimension), with a trainable spectral res","title":"Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-18T04:43:11Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2512.00242"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e3d53cd68bd92ada8cd78a3a3e467a51dac7156e18c32a5c4d4353bce67e21e1e0f766c87891ab8b5e5c65a7c73e0a958248a9c80699dd566508ec9c60bb410b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-18T04:43:11Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2512.00242"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"0cda40e305fc01a12d280ea27bea17dd663422f976e725807926141046722f74","leaf_index":140774,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"a08de9c24f4b85c88e9f850ecef6152ad632fbb665de445acb5973b0659fa031","side":"right"},{"sibling":"b5ae468824403bbe681d2494a5650b22980307a1541215345ca3e477f3e593a6","side":"left"},{"sibling":"4af419a0860369349fa4822f5d876d1e0167856fae640b01bc856473b9e154aa","side":"left"},{"sibling":"67827bc4d524f5f71a0e2717fb90ec69ed4d9969005f391d9208130f1195878a","side":"right"},{"sibling":"79e57fc8432578ac5a8b5e9f4bd401ede4f571493ff63adccccc7b99ae4373df","side":"right"},{"sibling":"b59f5b6589804050df943e9de027b74c1fffb33440b7e6dfcf198d1d29863180","side":"left"},{"sibling":"518d2c79e4bbff1e18ea05bbb3663a3fb58b3b1682a658f34e706ea23e091089","side":"left"},{"sibling":"30c60828b6b0ade79197e585b88c06ccf4f348c1e62fbf6710d89ae2c2e9dcfb","side":"left"},{"sibling":"6bedf73520cf3dd8758d8bdedf3be245de9aea97abd42934aae25539176ae1b2","side":"left"},{"sibling":"07abc3bad689e74e6304772503dc9372a118e6f66883b8e88c43414efddac063","side":"right"},{"sibling":"28b78fb112bcf26b6801664db97eb8f52a9bccbf0a7ae6766e11845d443692df","side":"left"},{"sibling":"68d0a4634c1460a19c92edd9480df3aa733b814463e7420d1e14471bf61b2f83","side":"right"},{"sibling":"8af64f275b862349aa3bbb9d5cd7fa9a7fdd5620af3bf1b36b2a4519b0b53bdf","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"b98c2afadb358e5387e88f19588f8343a81b488d9b44a6f7e57a032db3a1b030","side":"right"},{"sibling":"11b0c1591747f09f7c8971a6caa19befcd81317ca9dfd417b143234df4e10c79","side":"right"},{"sibling":"87206f3bcc342797c990d87f7235c01f78d32ca59cfaf8ad18d71afc879ba477","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":140892,"merkle_root":"6cca56ead155990456b8a014cc50bddbe710f409b26e3d1bfa6fb12b0bfcf6bf","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260518T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-18T05:37:30Z","sig_algorithm":"ed25519","signature":"1e1135f7595f79b14fb11f5fa81a2e17ad31b11b44b427a5e40a7d511cd86447daf492babd368ab571cf26404c8c74c450d460130fca4b064eb2760367489a0f","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_2eab85b4967cb7189c583cd148805094ba394b77f17643fe0117cba313e0d5fd"}}