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

arXiv: https://arxiv.org/abs/2608.19817 · HTML: https://mlsanity.com/paper/2608.19817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [Selective Kernel Networks](https://mlsanity.com/paper/1903.06586/) (2019)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity](https://mlsanity.com/paper/2207.03620/) (2022)
- [Pixel-Adaptive Convolutional Neural Networks](https://mlsanity.com/paper/1904.05373/) (2019)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Involution: Inverting the Inherence of Convolution for Visual Recognition](https://mlsanity.com/paper/2103.06255/) (2021)
- [Decoupled Dynamic Filter Networks](https://mlsanity.com/paper/2104.14107/) (2021)
- [Poly Kernel Inception Network for Remote Sensing Detection](https://mlsanity.com/paper/2403.06258/) (2024)
- [WeightNet: Revisiting the Design Space of Weight Networks](https://mlsanity.com/paper/2007.11823/) (2020)
- [Frequency Dynamic Convolution for Dense Image Prediction](https://mlsanity.com/paper/2503.18783/) (2025)
- [SMPConv: Self-moving Point Representations for Continuous Convolution](https://mlsanity.com/paper/2304.02330/) (2023)
- [KernelWarehouse: Rethinking the Design of Dynamic Convolution](https://mlsanity.com/paper/2406.07879/) (2024)
- [KAC: Kolmogorov-Arnold Classifier for Continual Learning](https://mlsanity.com/paper/2503.21076/) (2025)

## Abstract (arXiv)

Conventional convolutional kernels are typically defined on fixed discrete grids, limiting their ability to accommodate heterogeneous local structures. Existing adaptive operators improve flexibility but often couple geometric scale variation with content-dependent filtering, while incurring high computational cost from per-location kernel generation. To decouple geometric scale adaptation from content-dependent filtering while avoiding expensive per-location kernel generation, we propose Continuous Relative-scale KAN (Core-KAN), a relative-scale-conditioned continuous convolution operator. Core-KAN maps input features into a compact latent basis space and uses a lightweight scale controller to predict local scales relative to an exponential moving average reference. A KAN-based generator represents depth-wise kernel bases as continuous coordinate functions, allowing the operator to synthesize spatial filters at arbitrary resolutions rather than being confined to a fixed lattice. Instead of synthesizing independent kernels at every location, it constructs a compact bank of scale-conditioned kernel responses and interpolates them according to the predicted local scale map. An independent mixing controller further combines the interpolated basis responses based on local content, explicitly decoupling geometric scale adaptation from content-dependent filtering. Together with lightweight pointwise projections, this design forms a low-rank dynamic convolution that scales efficiently with kernel size and integrates readily into hierarchical vision backbones. Experiments across three representative vision tasks show Core-KAN consistently outperforms strong convolutional and dynamic-kernel baselines with only marginal parameter and computational overhead, offering an efficient, general framework for continuous, scale-adaptive convolution.