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

arXiv: https://arxiv.org/abs/2606.19538 · HTML: https://mlsanity.com/paper/2606.19538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 105 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [Benchmarking Robustness of 3D Point Cloud Recognition Against Common Corruptions](https://mlsanity.com/paper/2201.12296/) (2022)

## Abstract (arXiv)

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.