Unifying Convolution and Attention via Convolutional Nearest Neighbors

The shift from Convolutional Neural Networks to Transformers has reshaped computer vision, yet these two architectural families are typically viewed as fundamentally distinct. Convolutional Neural Networks are defined by spatially local convolution operations, while Transformers rely on global self-attention. We argue that convolution and self-attention, despite their apparent differences, can be unified within a single k-nearest neighbor aggregation framework. The critical insight is that both operations are special cases of neighbor selection and weighted aggregation. Convolution selects neighbors by spatial proximity while self-attention selects by feature similarity, revealing that they lie on a continuous spectrum rather than representing categorically different computations. We introduce Convolutional Nearest Neighbors (ConvNN), a unified framework that formalizes this connection. ConvNN exactly recovers standard and depthwise convolution by restricting neighbor selection to normalized spatial coordinates, and exactly recovers self-attention and its sparse variants, including KVT-attention, by replacing spatial proximity with scaled dot-product similarity. Beyond these special cases, ConvNN serves as a drop-in replacement for both convolution and attention layers, enabling systematic exploration of the intermediate spectrum between local and global aggregation through configurable similarity functions, neighbor selection strategies, positional encodings, and aggregation kernels.

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.

Superpixel-based image classification has traditionally leveraged graph neural networks (GNNs) for processing irregular image representations. Recent advances in computer vision, driven by Vision Transformers (ViTs), have introduced new paradigms in self-attentional models, surpassing convolutional neural networks (CNNs) in various tasks. However, a synergistic connection between GNNs, superpixels, and transformers remains unexplored. In this work, we propose Superpixel Transformers (SPT), a novel framework that unifies superpixel-based image classification and ViTs. SPT generalizes the Superpixel Image Classification with Graph Attention Networks (SICGAT) model and ViT to support arbitrary superpixel-based chunking strategies, connectivity graphs, and positional encodings. We introduce refinements including a multidimensional sine-cosine positional encoding and an enriched patch data structure that fully incorporates superpixel shape and color information. By testing SPT across datasets such as CIFAR10, FashionMNIST, and Imagenette, with various superpixel generation and graph connectivity strategies, we demonstrate that SPT achieves superior performance compared to previous superpixel-based GNN methods and remains competitive with ViTs. Notably, our approach addresses the limitations of SICGAT, such as information loss during pixel aggregation, and shows how constrained graph connectivity can enhance ViT performance. SPT bridges the gap between superpixel-based and transformer models, opening avenues for cross-domain generalization and future innovations in hybrid attentional frameworks, and showing that an image can also be worth $16\times16$ superpixels.