Light-ResKAN: A Parameter-Sharing Lightweight KAN with Gram Polynomials for Efficient SAR Image Recognition

Pan Yi; Weijie Li; Xiaodong Chen; Jiehua Zhang; Li Liu; Yongxiang Liu

cs.CVApr 2, 2026

Light-ResKAN: A Parameter-Sharing Lightweight KAN with Gram Polynomials for Efficient SAR Image Recognition

Authors: Pan Yi, Weijie Li, Xiaodong Chen, Jiehua Zhang, Li Liu, Yongxiang Liu

Organizations: The authors are with the College of Electronic Science and Technology, National University of Defense Technology, Changsha, 410073, China.

Abstract

Synthetic Aperture Radar (SAR) image recognition is vital for disaster monitoring, military reconnaissance, and ocean observation. However, large SAR image sizes hinder deep learning deployment on resource-constrained edge devices, and existing lightweight models struggle to balance high-precision feature extraction with low computational requirements. The emerging Kolmogorov-Arnold Network (KAN) enhances fitting by replacing fixed activations with learnable ones, reducing parameters and computation. Inspired by KAN, we propose Light-ResKAN to achieve a better balance between precision and efficiency. First, Light-ResKAN modifies ResNet by replacing convolutions with KAN convolutions, enabling adaptive feature extraction for SAR images. Second, we use Gram Polynomials as activations, which are well-suited for SAR data to capture complex non-linear relationships. Third, we employ a parameter-sharing strategy: each kernel shares parameters per channel, preserving unique features while reducing parameters and FLOPs. Our model achieves 99.09%, 93.01%, and 97.26% accuracy on MSTAR, FUSAR-Ship, and SAR-ACD datasets, respectively. Experiments on MSTAR resized to $1024 \times 1024$ show that compared to VGG16, our model reduces FLOPs by $82.90 \times$ and parameters by $163.78 \times$ . This work establishes an efficient solution for edge SAR image recognition.

Figures & tables

Fig. 1: Comparison of our proposed method with existing methods in terms of FLOPs and accuracy. The size of the circle represents the parameter size of the method. The graph shows the excellent balance between accuracy and computational resources of our method evaluated on MSTAR dataset resized to

1024\times 1024

. Compared to the traditional VGG16 architecture, Light-ResKAN achieves a 0.12% increase in accuracy while demonstrating significant computational and parameter efficiency, evidenced by an 82.90 times reduction in FLOPs and a 163.78 times reduction in parameter count.

Features	CNN	Transformer	KAN
Computational Complexity	Generally related to image dimensions and kernel size	Quadratic (with respect to sequence length)	Linear (with respect to input dimensionality), dependent on the form of activation functions
Parameter Efficiency	Relatively efficient via weight sharing	Parameters can be large, especially for deep or wide networks	High parameter efficiency depends on the form of the activation functions
Advantages	Strong visual feature extraction, relatively high computational efficiency	Powerful long-range dependency modeling, good parallelism	Low parameter count, computationally efficient, highly interpretable, strong expressive power, easy integration
Disadvantages	Limited global information fusion capability	High computational complexity, large parameter count, challenges in processing long sequences	Emerging field, requires extensive validation and optimization

TABLE I: Comparison of CNN, Transformer, and KAN

Methods	Application Fields	Datasets	Activation Functions
KCN	Remote Sensing Scene Classification	EuroSAT	Spline
SpectralKAN	Hyperspectral Image Change Detection	Farmland, river, USA; Bay Area, Santa Barbara	Spline
WaveKAN	Hyperspectral Image Classification	Salinas, Pavia, Indian Pines	Wavelet
U-KAN	Agricultural Land Segmentation	South Africa Crop Type, Sentinel-1 and Sentinel-2	Spline

TABLE II: Overview of KAN-Based Methods and Their Application Fields

Fig. 2: Model architecture diagram of Light-ResKAN. (a) Provides its framework with three main modules: the shared activation function convolution $\phi_{n\times n}$ , Bottleneck ResKAGN 1 and Bottleneck ResKAGN 2. (b) Details the internal structure of the shared activation function convolution $\phi_{n\times n}$ . (c) Illustrates the architecture of Bottleneck ResKAGN 1 and Bottleneck ResKAGN 2. (d) Provides a symbol List.

Fig. 3: An example of $\phi_{2\times 2}$ convolution in one channel. (a) The operation process and result of initial KAN convolution. (b) The operation process and result of the proposed $\phi_{2\times 2}$ convolution with shared weights. Among them, ${y}_{1}={\phi}_{11}\left({a}_{1}\right)+{\phi}_{12}\left({a}_{2}\right)+{\phi}_{21}\left({a}_{3}\right)+{\phi}_{22}\left({a}_{4}\right)$ and ${f}_{1}=\phi\left({a}_{1}\right)+\phi\left({a}_{2}\right)+\phi\left({a}_{3}\right)+\phi\left({a}_{4}\right)$

Super-classes	Fine-classes	Number
		Train (17°)	Test (15°)
Rocker launcher	2S1	299	274
Air defense unit	ZSU23/4	299	274
Trunk	ZIL131	299	274
Bulldozer	D7	299	274
Tank	T62	299	273

TABLE III: The number of training and testing sets under MSTAR

Super-classes	Fine-classes	Number
		Train	Test
Ships	Cargo	366	156
	Fishing	248	106
	Tanker	150	64
	Other ships	312	133
Lands	Bridges	1023	438

TABLE IV: The number of training and testing sets under FUSAR-Ship

Aircraft types	Number
	Train	Test
A220	325	139
A330	359	153
A320321	357	153
ARJ21	360	154
Boeing737	370	158

TABLE V: The number of training and testing sets under SAR-ACD

Fig. 4: Three SAR datasets. (a) Ten types of SAR images in MSTAR. (b) Ten types of SAR images in FUSAR-Ship. (c) Six types of SAR images in SAR-ACD.

Models	Year	Pars. (M)	Size (MB)	Accuracy (%)			FLOPs (G)			Test time (ms)
Models				MSTAR	FUSAR-Ship	SAR-ACD	MSTAR	FUSAR-Ship	SAR-ACD	MSTAR	FUSAR-Ship	SAR-ACD
AlexNet [ 60 ]	2012	57.04	228.18	97.44	89.41	95.76	0.19	3.71	0.19	9.54	30.32	9.53
VGG16 [ 61 ]	2015	134.30	537.21	96.59	90.73	96.17	4.07	80.37	4.07	11.42	43.72	11.40
ResNet18 [ 62 ]	2016	11.18	44.73	96.71	83.54	95.34	0.49	9.51	0.49	10.31	32.41	10.29
ResNet50 [ 62 ]	2016	23.53	94.11	97.13	86.71	96.69	1.08	21.35	1.08	10.92	32.93	10.91
ConvNeXt [ 63 ]	2022	87.58	350.23	96.04	77.86	95.83	4.07	80.53	4.07	17.23	53.25	17.19

TABLE VI: Comparison of the Proposed Model with Different Models on Three SAR Datasets.

Models	Accuracy (%)	FLOPs (G)	Test time (ms)
AlexNet [ 60 ]	99.38	15.01	86.31
VGG16 [ 61 ]	99.34	320.83	131.50
ResNet18 [ 62 ]	99.05	38.01	90.47
ResNet50 [ 62 ]	99.17	86.58	101.47
ConvNeXt [ 63 ]	98.76	321.47	166.58
MACN [ 64 ]	92.53	49.48	956.23

TABLE VII: Performance Comparison of Different Models on MSTAR Dataset Resized to

1024\times 1024

Fig. 5: t-SNE visualization results of different methods on MSTAR dataset. (a) ASANet. (b) ConvnNeXt. (c) MACN. (d) VGG16. (e) Cross-HL. (f) Light-ResKAN (Ours). Colors represent different categories, and the distribution density of points and the compactness of clusters indicate the discriminative ability of the model for this task. The results indicate that Light-ResKAN can achieve the most compact intra class clusters and the most obvious inter class separation under the same data distribution, demonstrating stronger feature expression ability and higher classification performance.

Fig. 6: Probability density image of Gamma distribution.

\alpha

= 3,

\beta

= 0.1: the Gamma distribution exhibits a relatively sharp peak, concentrated at lower values, with a short tail that gradually declines.

\alpha

= 1,

\beta

= 0.5: the Gamma distribution becomes more diffuse, with a flatter peak and a tail that gradually lengthens.

\alpha

= 0.5,

\beta

= 2: the Gamma distribution presents a flattened and broad shape, with a longer tail and a lower peak.

Fig. 7: Comparison of images with different levels of noise. (a) Original image. (b)Image with weak noise added. (c) Image with medium noise added. (d) Image with strong noise added.

Fig. 8: Experimental results of different models under different noise intensities on three SAR datasets. The accuracy decreases as the perturbation intensity increases, and our method maintains better robustness under different parameters than others.

	K-C	G-P	B-K-C	S-A-F	MSTAR	FUSAR-Ship	SAR-ACD
ResNet	$\times$	$\times$	$\times$	$\times$	97.13	86.71	96.69
	$\checkmark$	$\times$	$\times$	$\times$	96.06	90.44	95.13
	$\checkmark$	$\checkmark$	$\times$	$\times$	97.56	91.23	96.87
	$\checkmark$	$\checkmark$	$\checkmark$	$\times$	98.22	91.58	97.07
	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	99.09	93.01	97.26

TABLE VIII: Impact of Key Components: Ablation Experiments on Model Performance. (K-C:KAN convolution, G-P: Gram Polynomials, B-K-C: Bottleneck KAGN convolution, S-A-F: shared activation function)

Basis Functions	MSTAR	FUSAR-Ship	SAR-ACD
Spline Function	96.17	90.45	93.15
Chebyshev Polynomials	93.94	86.04	92.81
Legendre Polynomials	97.33	91.36	96.94
Radial Basis	92.95	91.84	91.00
Gram Polynomials	99.09	93.01	97.26

TABLE IX: Accuracy of Different Basis Functions on SAR Datasets

Models	MSTAR (N-Shot)
	5	10	20
AlexNet [ 60 ]	38.48	46.95	57.64
VGG16 [ 61 ]	37.26	45.36	55.26
ResNet18 [ 62 ]	41.57	52.57	59.51
ResNet50 [ 62 ]	38.58	51.26	58.53
ConvNeXt [ 63 ]	27.36	38.02	51.37

TABLE X: Performance of Different Models on MSTAR Dataset (N-Shot).

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