Kolmogorov-Arnold Attention: Is Learnable Attention Better For Vision Transformers? (2503.10632v2)

Abstract: Kolmogorov-Arnold networks (KANs) are a remarkable innovation consisting of learnable activation functions with the potential to capture more complex relationships from data. Presently, KANs are deployed by replacing multilayer perceptrons (MLPs) in deep networks, including advanced architectures such as vision Transformers (ViTs). This work asks whether a similar replacement in the attention can bring benefits. In this paper, we design the first learnable attention called Kolmogorov-Arnold Attention (KArAt) for ViTs that can operate on any basis, ranging from Fourier, Wavelets, Splines, to Rational Functions. However, learnable activations in attention cause a memory explosion. To remedy this, we propose a modular version of KArAt that uses a low-rank approximation. By adopting the Fourier basis, Fourier-KArAt and its variants, in some cases, outperform their traditional softmax counterparts, or show comparable performance on CIFAR-10, CIFAR-100, and ImageNet-1K datasets. We also deploy Fourier KArAt to ConViT and Swin-Transformer, and use it in detection and segmentation with ViT-Det. We dissect these architectures' performance by analyzing their loss landscapes, weight distributions, optimizer path, attention visualization, and transferability to other datasets. KArAt's learnable activation shows a better attention score across all ViTs, indicating better token-to-token interactions, contributing to better inference. Still, its generalizability does not scale with larger ViTs. However, many factors, including the present computing interface, affect the performance of parameter- and memory-heavy KArAts. We note that the goal of this paper is not to produce efficient attention or challenge the traditional activations; by designing KArAt, we are the first to show that attention can be learned and encourage researchers to explore KArAt in conjunction with more advanced architectures.