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

[Submitted on 17 Jun 2026 (v1), last revised 27 Jun 2026 (this version, v3)]

View PDF HTML (experimental)

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.

Submission history

From: Ashim Dhor [view email]
[v1] Wed, 17 Jun 2026 19:30:11 UTC (228 KB)
[v2] Fri, 19 Jun 2026 20:29:57 UTC (228 KB)
[v3] Sat, 27 Jun 2026 14:18:49 UTC (228 KB)