Core-KAN: Continuous Vision Kernels with Kolmogorov-Arnold Networks

Traditional convolutional networks rely on fixed discrete kernels shared across all spatial locations. While this design provides translation equivariance and computational efficiency, it restricts the network's ability to adapt to heterogeneous local structures such as object boundaries, fine textures, and varying object scales. Although various adaptive and dynamic convolution operators have been proposed to address this limitation, they typically couple geometric scale variations with content-dependent filtering and incur heavy computational overheads by generating independent kernels at every spatial location. This paper investigates whether an efficient continuous convolution operator can be constructed by explicitly decoupling geometric scale adaptation from content-dependent composition using Kolmogorov-Arnold Networks (KANs).

The authors propose Continuous Relative-scale KAN (Core-KAN), a novel relative-scale-conditioned continuous convolution operator. Instead of synthesizing unique kernels at every position, Core-KAN maps input features into a compact latent basis space and employs a dual-control mechanism. A lightweight scale controller predicts dense local scales normalized against an operator-specific exponential moving average (EMA) reference. Simultaneously, a shared KAN parameterizes depthwise kernel bases as continuous coordinate functions. By sampling this continuous kernel field at a small, fixed set of scale supports and utilizing a support-and-interpolate scheme, Core-KAN constructs a response bank without per-location kernel generation. An independent mixing controller then combines these interpolated basis responses based on local content, ensuring that geometric scale adaptation and content-dependent filtering operate independently.

Extensive experiments demonstrate that Core-KAN consistently outperforms strong convolutional and dynamic-kernel baselines across diverse computer vision benchmarks while introducing only marginal parameter and computational overhead. On the ImageNet-1K classification benchmark, a ResNet-50 backbone integrated with Core-KAN achieves higher Top-1 accuracy than established operators like ODConv, DY-Conv, and KernelWarehouse. Furthermore, experiments on the COCO dataset using Mask R-CNN under both standard 1x and 3x training schedules show consistent performance gains in bounding box average precision and mask average precision for object detection and instance segmentation.