Interpolation between Convolution and Attention via K-Nearest Neighbors

Convolutional Neural Networks and Vision Transformers are the two dominant architectural families in computer vision, defined by spatially local convolution and global self-attention respectively. Despite their apparent differences, we show that both operations are special cases of a single $k$-nearest neighbor aggregation framework: convolution selects neighbors by spatial proximity while attention selects by feature similarity, placing them at two ends of a shared operational spectrum. We introduce Convolutional Nearest Neighbors (ConvNN), a unified framework that exactly recovers standard and depthwise convolution, self-attention, and sparse attention variants including KVT-attention as special cases, and exposes the design space of neighbor-selection strategies between them through configurable similarity functions, positional encodings, and aggregation kernels. We validate ConvNN on ImageNet-1K classification across two complementary architectures: a hybrid branching layer in ResNet-50 that combines local and global feature learning, improving top-1 accuracy by 3.0% over the ResNet-50 baseline, and ConvNN-attention in ViT-Base that achieves 81.64% top-1 accuracy, surpassing standard multi-head self-attention by 0.7%. Together, these results demonstrate that ConvNN provides a principled foundation for designing operations that bridge convolutional and attention-based computation.

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.

Large language models (LLMs) largely rely on Transformers, where self-attention provides global token interaction but does not explicitly encode the locality of natural language. We study whether lightweight depthwise convolutions can supply this local inductive bias without materially increasing model size. Our macro-level ablation compares convolution at 17 locations in a Qwen3 Transformer block and finds the best results when convolution is applied to the projected queries, keys, and values before attention. A subsequent micro-level study favors a residual depthwise convolution with kernel size $k=3$, without additional normalization or activation. Across Qwen3 models and several pre-training data budgets, this design improves the average accuracy on seven downstream benchmarks while adding less than $0.01\%$ parameters. A representation-level case study further suggests that the convolution makes repeated token IDs more sensitive to their immediate context. These results support depthwise convolution as a lightweight complement to self-attention for modeling short-range token interactions.