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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 para","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:2606.19538v3 Announce Type: replace \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 para","title":"ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-30T04:43:04Z","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":"ed25519:7c3311610cfc13216bb782449c771c5e0dc33e1faf5c97578e7ec2a1a6aac981c1cbbc41af61d3712d8f54e184f4e61d9e240b2659f3785f0a41c06682e5410e","signer":"crovia.substrate","subject":{"observed_at":"2026-06-30T04:43:04Z","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":"fb6dabe7804724ef0f236edf6cc21101531ac24a9b5444990155ad34bb09ca55","leaf_index":265080,"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":"8e850a79d05aa289959c8da7be5c6557c6157fe25955106dd3df5f0a3c312ccf","side":"right"},{"sibling":"717cccbf3f31be2a589d842af67cf6563d760049d1cd730e32e4a092b6d062bb","side":"right"},{"sibling":"d4ea0726aa15df33ae31627fb8b06e30f585cf25393d872c6e79e3aa8125b824","side":"right"},{"sibling":"38af5e572d544c21b83ba23701d1bcb883fa84252c4f5666873b821f5282a7a9","side":"left"},{"sibling":"08c7ad9e9607fd23cb10efd0771c7e9ff3239fc378471c8d7af1893b74df0a83","side":"left"},{"sibling":"efb82cdea382869d8079c65027e0062af462c36eac5f26f73ea2c40736ab76db","side":"left"},{"sibling":"5b8a0910e4e94e2a9b10497e13f92efba841a089742fa095b3d09b024957b4bc","side":"left"},{"sibling":"e3ac74800103452465231dd60eaf9671a5039238ce21e35760b324bd56f70d4e","side":"right"},{"sibling":"3f337e26f1a0c4c64b8b7ebac04427325a7e7838c802c162576de1cd617b91ce","side":"left"},{"sibling":"1549a8883ab3267f958dc2624919e40c65c82958b8005967ed6a4da1247da0ad","side":"left"},{"sibling":"23994bf0974e5c9c7f63a61b4f0a48b0ca756a4adc34a8f85f878e774c37dfbe","side":"right"},{"sibling":"f9b4bed84fa6990c71ad2887c91bda183001f05f6b648f21d1273045a26b11fd","side":"left"},{"sibling":"173d2dc4b29ee04ea41d6d0ebc334c4bc2d46e7ee4230c94765413f24fb4bc42","side":"right"},{"sibling":"112461f7c0ec411116fb5c6c90fe95cea9d8f188b9fe08afe25a837ac02d0071","side":"right"},{"sibling":"ea9488204352c49db8f7daf05eefcd7628ecf9413830346674801a99d0654a94","side":"right"},{"sibling":"6261c13b9922cb657f10d1e5d36ec15d8771cf8766e36c61dcbffb7bed57e396","side":"right"},{"sibling":"fa19aa3faf287618b820bcfceebb366152ad521dd20ef9f51e977816663e448b","side":"right"},{"sibling":"c32f943406b62d1fc59b7f7e243492174c8e1caba8c8a2705f86c773315736e0","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":265374,"merkle_root":"9636001ecab173cb6af10dc7c71eb14585daa62f9c0a6f027046f05633156891","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260630T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-30T05:38:03Z","sig_algorithm":"ed25519","signature":"6d4b8fd9b9da856cbb5fba7540877c6a63fa18a5ec3eaf28dc4d6d1c64921c9c0565f8c95f4b7aec0e7744fd7754844f051baf863db708cad768765b416a7b0c","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_96f265ee45a6aa9bc9087bd89bd21d5f0bdb75627da89cb26d68a52168762702"}}