2026-06-19原文2 min readUpdated: 2026-06-19

ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

This paper introduces the Integral Transform Network (ITNet), a unified architecture that generalizes convolution, self-attention, and recurrence through a learnable integral kernel. ITNet matches or exceeds specialized models on multiple benchmarks.

SourcearXiv AIAuthor: Ashim Dhor, Rasel Mondal, Pin Yu Chen

[2606.19538] ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

[Submitted on 17 Jun 2026]

Title:ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

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Abstract: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 parameterizations, and that ITNet is a universal approximator of continuous operators. To make this practical, we develop tiled kernel fusion, importance-weighted Monte Carlo integration, and learned low-rank factorization, enabling efficient and scalable computation. A single ITNet architecture with a shared operator and lightweight modality-specific encoders matches or exceeds specialized baselines on ImageNet-1K , GLUE, ModelNet40, VQA\,v2 and NLVR2. The results demonstrate that a single learned interaction mechanism can recover the behavior of all three architectural families from data.

Subjects:

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

Cite as: arXiv:2606.19538 [cs.AI]

(or arXiv:2606.19538v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2606.19538

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Ashim Dhor [view email] [v1] Wed, 17 Jun 2026 19:30:11 UTC (228 KB)

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