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We show that this fragmentation reflects not a fundamental diversity in how signals should be processed, but rather incomplete views of a single underlying mathematical object: a learnable integral transform. We introduce the Integral Transform Network (ITNet), a unified architecture built around a learnable kernel that depends jointly on positions and features. This kernel is implemented as a small neural network, specifically an MLP, that models pairwise interactions, enabling the model to adapt its behavior from data. We show that convolution, self-attention (including multi-head), and autoregressive recurrence (including LSTM, GRU, S4, and Mamba) arise as special cases under appropriate paramete","title":"ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence","url":"https://arxiv.org/abs/2606.19538","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.19538v1 Announce Type: new \nAbstract: Convolutional networks, recurrent networks, and transformers each encode different inductive biases -- locality, sequential memory, and content-dependent pairwise interaction -- and have remained mathematically distinct since their inception. We show that this fragmentation reflects not a fundamental diversity in how signals should be processed, but rather incomplete views of a single underlying mathematical object: a learnable integral transform. We introduce the Integral Transform Network (ITNet), a unified architecture built around a learnable kernel that depends jointly on positions and features. This kernel is implemented as a small neural network, specifically an MLP, that models pairwise interactions, enabling the model to adapt its behavior from data. We show that convolution, self-attention (including multi-head), and autoregressive recurrence (including LSTM, GRU, S4, and Mamba) arise as special cases under appropriate paramete","title":"ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-19T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.19538"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:3b299ce1053e90444b67b79036403740aee4a1d04bad03ebc3dd46a571f8aea4131f74212031381a8a7fce7c5c624a57c81384a260183ee76fff8309b7bbc204","signer":"crovia.substrate","subject":{"observed_at":"2026-06-19T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.19538"},"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":"2d619064252ef1cf97b66ffedaef71c0d877cd4fc12622e359685cc2b7b14d53","leaf_index":235464,"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":"e06beb950164236477566ceb34729e91401340debe7f7a38abf0c50caa41a804","side":"right"},{"sibling":"d305fdfa807eb38ff75bfdcf3c224b41322f61c2157737086ba630f2d0d7af4e","side":"right"},{"sibling":"f34524baf536cb76da80fdf418d956c08991be7da978e040802ae6de1586a859","side":"right"},{"sibling":"0c8ffb410affcb1ee44c49284e55c8bd7f4c5b25534e35fd3839a1815612e274","side":"left"},{"sibling":"03fc56070f0c5089bf6ede33ae0559da5ff3b395217f6cae545f79f7e34fc505","side":"right"},{"sibling":"bcc64a96b2351ef6571992656cd86c436090f98a58edd222113a9eab3bbe6e32","side":"right"},{"sibling":"696ac6bcf68966ee959b35539f0bed60b3216ccb53620defd29feb8dbcb2ac30","side":"left"},{"sibling":"95ba45f2fea2d822bc863962b7e478ea50086827d90fab88c0da065d454d7ac5","side":"left"},{"sibling":"00f27f149ddd2eb0d2cf60eaed9e1d55c662cf1cf69c95fbea03bba9d35f90c7","side":"left"},{"sibling":"797e0feb6bf826a55956c876711cd24824818c5a84a591f8cc06b95577b3405d","side":"left"},{"sibling":"f049d6e86b410f6f63921a6e3aa684efffa398fd23eed28245c43b156d404c5f","side":"left"},{"sibling":"9ec7f4f84de7e2057a02ac55686567b21acfd5beaecc7a84e9e48f3db17296c2","side":"right"},{"sibling":"410c633928fea11c5b4bdddb431956b1d7c320db9cda00d2fe32e0fcf888d7b7","side":"left"},{"sibling":"b52a771530dd1686bca49e42088898b86da94879579cd6a995c6ab0598a665fe","side":"right"},{"sibling":"a116bb92f9b0350491155b470acc86d006c33ec558759e49e56614a54c39f242","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"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":241122,"merkle_root":"7a906c6a26ff6c6feabc2feaba6a1a70c515e6fd72a38c779293b0f78ff291c4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260622T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-23T06:25:25Z","sig_algorithm":"ed25519","signature":"5576b1d56d5dbb0d96c780fa3ca0940d805c8de95c6251bc87297f0be058aa5e37eb53a6aa1b601381f489f093842cf674b28737ed8e46ce3a49814b5e57290c","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_560c3b78605f20e8582e3ffae31e1b72b5f1f80df3ef307ab3974e3bd9952f95"}}