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

Lan Guo; Mengling Li; Haoran Li; Jun Shen; Yuanbo Jiang; Qingguo Zhou; Binbin Yong

cs.CVAug 20, 2026

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

Authors: Lan Guo, Mengling Li, Haoran Li, Jun Shen, Yuanbo Jiang, Qingguo Zhou, Binbin Yong

Organizations: School of Information Science and Engineering, Lanzhou University · Department of Data Science and AI, Monash University · School of Computing and Information Technology, University of Wollongong

Abstract

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.

Figures & tables

Figure 1: Conceptual comparison between conventional convolution and Core-KAN. (a) Conventional convolution shares a fixed discrete kernel across locations. (b) Core-KAN conditions a shared KAN-parameterized continuous kernel field on local relative scales and independently mixes basis responses according to content, enabling location-specific aggregation on a fixed sampling grid. Implementation details are omitted for clarity.

Figure 2: Overview of Core-KAN. The scale controller predicts a dense scale field $\alpha(p)$ , and an operator-specific EMA reference $\mu_{\alpha}$ converts absolute scale supports into relative supports. These supports transform a predefined coordinate grid $q$ before it is evaluated by the KAN kernel generator. The learnable spline parameters $\theta$ define $N$ shared continuous kernel fields, from which $M$ sets of fixed-size kernels are sampled. Depthwise convolution produces a response bank $\mathcal{R}$ , and each location interpolates its two neighboring support responses.

Figure 3: Pixel-wise scale interpolation in response space. For a location $p$ with $s_{j}\leq s(p)\leq s_{j+1}$ , Core-KAN retrieves the neighboring support responses $R_{j,n}(p)$ and $R_{j+1,n}(p)$ and linearly combines them using weights $1-\lambda_{p}$ and $\lambda_{p}$ , respectively. Batch indices are omitted for clarity.

Method	Params (M) $\downarrow$	Top-1 (%) $\uparrow$	Top-5 (%) $\uparrow$
ResNet-50 [CVPR’16]	25.56	78.44	94.24
DY-Conv [CVPR’20]	100.88	79.00	94.27
ODConv [ICLR’22]	90.67	78.52	94.01
SCConv [CVPR’23]	17.69	79.89	94.76
RefConv [TNNLS’25]	36.97	79.91	94.61
PartialNet [AAAI’26]	18.00	80.61	95.13

Table 1: ImageNet-1K validation results. Reported or reproduced training recipes differ across methods, so the table is intended as a reference comparison. Bold and underlined values indicate the best and second-best accuracy, respectively.

Method	Object Detection						Instance Segmentation
Method	$\mathrm{AP}^{\mathrm{box}}$	$\mathrm{AP}^{\mathrm{box}}_{50}$	$\mathrm{AP}^{\mathrm{box}}_{75}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{S}}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{M}}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{L}}$	$\mathrm{AP}^{\mathrm{mask}}$	$\mathrm{AP}^{\mathrm{mask}}_{50}$	$\mathrm{AP}^{\mathrm{mask}}_{75}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{S}}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{M}}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{L}}$
ResNet-50 [CVPR’16]	37.9	58.7	41.2	21.6	41.5	49.3	34.5	55.6	36.8	15.9	37.1	50.4
DY-Conv [CVPR’20]	39.2	60.3	42.5	23.0	42.9	51.4	34.7	56.0	37.1	16.4	36.9	51.1
ODConv [ICLR’22]	40.1	61.5	43.6	24.0	43.6	52.3	36.7	58.5	39.6	18.6	39.0	52.8
KernelWarehouse [ICML’24]	42.4	65.4	46.3	27.2	46.2	54.6	38.9	62.0	41.5	22.7	42.6	53.1
FDConv [CVPR’25]	42.5	64.8	46.2	26.4	47.0	54.9	38.3	61.8	41.0	19.6	42.4	54.3

Table 2: COCO val2017 results using Mask R-CNN under the standard

1\times

schedule (12 epochs). Bold and underlined values denote the best and second-best results, respectively; ties are marked equally.

Method	Object Detection						Instance Segmentation
Method	$\mathrm{AP}^{\mathrm{box}}$	$\mathrm{AP}^{\mathrm{box}}_{50}$	$\mathrm{AP}^{\mathrm{box}}_{75}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{S}}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{M}}$	$\mathrm{AP}^{\mathrm{box}}_{\mathrm{L}}$	$\mathrm{AP}^{\mathrm{mask}}$	$\mathrm{AP}^{\mathrm{mask}}_{50}$	$\mathrm{AP}^{\mathrm{mask}}_{75}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{S}}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{M}}$	$\mathrm{AP}^{\mathrm{mask}}_{\mathrm{L}}$
ResNet-50 [CVPR’16]	40.9	61.3	44.8	24.4	44.6	52.3	37.1	58.3	39.9	18.4	39.8	52.9
DY-Conv [CVPR’20]	41.9	63.0	45.7	25.8	45.6	53.8	36.9	58.5	39.7	18.8	39.4	53.2
ODConv [ICLR’22]	42.6	64.0	46.6	27.0	46.3	54.8	38.7	60.6	42.0	21.4	41.2	54.7
KernelWarehouse [ICML’24]	45.6	67.5	49.8	29.8	49.4	59.0	41.5	63.0	44.8	24.2	43.9	58.5
FDConv [CVPR’25]	45.7	67.3	50.4	30.5	49.7	58.4	41.7	62.5	45.0	24.0	44.2	58.7

Table 3: COCO val2017 results using Mask R-CNN under the standard

3\times

schedule (36 epochs). Bold and underlined values denote the best and second-best results, respectively; ties are marked equally.

Method	Params (M) $\downarrow$	mIoU (%) $\uparrow$	mAcc (%) $\uparrow$
ResNet-50 [CVPR’16]	66.00	40.00	49.61
DY-Conv [CVPR’20]	140.00	41.20	51.05
ODConv [ICLR’22]	131.00	42.36	52.51
KernelWarehouse [ICML’24]	141.00	43.20	53.30
FDConv [CVPR’25]	70.00	43.50	53.63
Core-KAN (Ours)	68.50	44.19	54.38

Table 4: ADE20K validation results with a ResNet-50 backbone. Params denotes the complete segmentation model. Bold and underlined values denote the best and second-best results, respectively.

Figure 4: Evolution of learned $3\times 3$ kernels in the last Core-KAN block. (a) Four basis fields queried at five relative scales. (b) PCA trajectories of densely sampled kernels. (c) Relative Frobenius change between adjacent queries. Smooth, basis-specific trajectories indicate a continuous kernel field rather than a discrete lookup table.

Figure 5: Interpolation fidelity to direct continuous-kernel evaluation. (a) Relative output error across five scale quantiles for different support counts $M$ . (b) Mean, median, and 95th-percentile error. Denser supports consistently reduce the approximation error.

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