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arxiv: 2604.01903 · v2 · submitted 2026-04-02 · 💻 cs.CV

Recognition: unknown

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
Authors on Pith no claims yet

Pith reviewed 2026-05-13 22:17 UTC · model grok-4.3

classification 💻 cs.CV
keywords SAR image recognitionKolmogorov-Arnold NetworkGram polynomialslightweight modelparameter sharingResNetedge deploymentsynthetic aperture radar
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The pith

Light-ResKAN reaches 99.09% accuracy on SAR image datasets while cutting FLOPs by 82.9 times and parameters by 163.8 times compared to VGG16.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents Light-ResKAN as a lightweight variant of ResNet tailored for synthetic aperture radar image recognition. It replaces ordinary convolution layers with KAN convolutions that employ Gram polynomials as the learnable activation functions and introduces per-channel parameter sharing inside each kernel. This combination is intended to capture the complex non-linear patterns typical of SAR data while keeping the total number of trainable weights and arithmetic operations low enough for edge hardware. Experiments report top accuracies of 99.09 percent on MSTAR, 93.01 percent on FUSAR-Ship, and 97.26 percent on SAR-ACD, together with the stated efficiency gains on large 1024-by-1024 inputs. The central argument is that these architectural choices deliver a practical trade-off between recognition precision and computational cost for real-world SAR tasks such as disaster monitoring and reconnaissance.

Core claim

Light-ResKAN modifies the ResNet backbone by substituting standard convolutions with KAN convolutions that use Gram polynomials as activations and applies a per-channel parameter-sharing scheme inside each kernel. On the MSTAR, FUSAR-Ship, and SAR-ACD benchmarks the resulting model records 99.09 percent, 93.01 percent, and 97.26 percent accuracy respectively. When tested on 1024-by-1024 MSTAR images the same architecture reduces floating-point operations by a factor of 82.90 and trainable parameters by a factor of 163.78 relative to VGG16, while still preserving sufficient feature diversity for the reported classification performance.

What carries the argument

KAN convolution layers that replace fixed activations with Gram polynomials and enforce per-channel parameter sharing inside each kernel, allowing adaptive non-linear feature extraction at greatly reduced parameter count.

If this is right

  • SAR image classification at high accuracy becomes feasible on power- and memory-limited edge processors without cloud offloading.
  • The same Gram-polynomial KAN blocks can be inserted into other residual architectures to shrink model size for any large-resolution imagery task.
  • Per-channel sharing reduces redundancy without collapsing channel-specific information needed for distinguishing SAR targets.
  • The approach scales to 1024-by-1024 inputs while still delivering the stated order-of-magnitude savings in compute and storage.
  • Direct comparison on three public SAR benchmarks shows the method outperforms prior lightweight CNN baselines in the reported accuracy-efficiency trade-off.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The architecture could be tested on multi-temporal or multi-polarization SAR stacks to check whether the same efficiency gains hold when input dimensionality increases.
  • Replacing Gram polynomials with other orthogonal polynomial bases inside the KAN layers offers a simple ablation that would isolate the contribution of the chosen activation family.
  • Quantizing the already-reduced weights after training would be a natural next step to push the model further toward ultra-low-power microcontrollers.
  • The parameter-sharing pattern may generalize to transformer-style attention blocks, potentially yielding lightweight hybrid models for video SAR streams.

Load-bearing premise

Gram-polynomial activations together with per-channel parameter sharing will keep enough feature diversity in the network to match or exceed the accuracy of full-parameter CNNs on SAR imagery.

What would settle it

Measuring accuracy on the same MSTAR, FUSAR-Ship, or SAR-ACD splits after replacing the Gram-polynomial KAN layers with ordinary convolutions of matched capacity and confirming that accuracy rises substantially while the claimed FLOPs and parameter reductions disappear.

Figures

Figures reproduced from arXiv: 2604.01903 by Jiehua Zhang, Li Liu, Pan Yi, Weijie Li, Xiaodong Chen, Yongxiang Liu.

Figure 1
Figure 1. Figure 1: Comparison of our proposed method with existing methods in terms [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Model architecture diagram of Light-ResKAN. (a) Provides its framework with three main modules: the shared activation function convolution [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An example of ϕ2×2 convolution in one channel. (a) The operation process and result of initial KAN convolution. (b) The operation process and result of the proposed ϕ2×2 convolution with shared weights. Among them, y1 = ϕ11 (a1) + ϕ12 (a2) + ϕ21 (a3) + ϕ22 (a4) and f1 = ϕ (a1) + ϕ (a2) + ϕ (a3) + ϕ (a4) single activation function [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 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 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: t-SNE visualization results of different methods on MSTAR dataset. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Probability density image of Gamma distribution. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of images with different levels of noise. (a) Original [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Experimental results of different models under different noise intensities on three SAR datasets. The accuracy decreases as the perturbation intensity [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript introduces Light-ResKAN, a parameter-efficient modification of ResNet for SAR image recognition. It replaces convolutional layers with KAN convolutions that use Gram polynomials as activations and applies per-channel parameter sharing within kernels. The paper claims state-of-the-art accuracies of 99.09% on MSTAR, 93.01% on FUSAR-Ship, and 97.26% on SAR-ACD, while demonstrating 82.90× reduction in FLOPs and 163.78× in parameters compared to VGG16 on 1024×1024 images.

Significance. Should the empirical results prove robust, the approach represents a meaningful advance in lightweight deep learning for SAR imagery, potentially enabling real-time processing on edge hardware for applications like disaster monitoring and reconnaissance. The combination of KANs with Gram polynomials and sharing strategy offers a new direction for balancing expressivity and efficiency in convolutional networks.

major comments (3)
  1. Abstract: The central performance claims (99.09% accuracy on MSTAR, 82.90× FLOPs reduction vs. VGG16) rest on unreviewed empirical results with no training details, ablation studies, or error bars provided, undermining assessment of the accuracy-efficiency trade-off.
  2. Method (parameter-sharing description): The assertion that per-channel sharing 'preserves unique features while reducing parameters' is load-bearing for the efficiency claims, yet no analysis, visualization of learned functions, or ablation (shared vs. independent KAN activations per channel) is given to confirm feature diversity is maintained for SAR textures.
  3. Experiments: No ablation studies compare Gram polynomials to standard KAN activations or to baseline ResNet, and no details on how VGG16 was trained/adapted on the 1024×1024 resized MSTAR data are supplied, making the reported 163.78× parameter reduction difficult to interpret.
minor comments (1)
  1. Abstract: Dataset names (MSTAR, FUSAR-Ship, SAR-ACD) appear without citations or brief descriptions; adding these would improve clarity for readers outside the SAR community.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, providing clarifications from the manuscript where applicable and committing to revisions that strengthen the presentation of our results and methods.

read point-by-point responses

  1. Referee: Abstract: The central performance claims (99.09% accuracy on MSTAR, 82.90× FLOPs reduction vs. VGG16) rest on unreviewed empirical results with no training details, ablation studies, or error bars provided, undermining assessment of the accuracy-efficiency trade-off.

    Authors: The full training details, hyperparameters, data preprocessing steps, and ablation studies are described in Section 4 (Experiments) and the supplementary material. To make these more immediately accessible, we will revise the abstract to include a concise reference to the experimental protocol and report error bars as standard deviations computed over five independent runs. This will improve transparency without altering the core claims. revision: yes

  2. Referee: Method (parameter-sharing description): The assertion that per-channel sharing 'preserves unique features while reducing parameters' is load-bearing for the efficiency claims, yet no analysis, visualization of learned functions, or ablation (shared vs. independent KAN activations per channel) is given to confirm feature diversity is maintained for SAR textures.

    Authors: We agree that direct empirical support for the parameter-sharing mechanism would strengthen the paper. In the revised manuscript we will add an ablation comparing per-channel shared KAN activations against fully independent activations per channel, together with visualizations of the learned Gram polynomial basis functions across channels. These additions will demonstrate that feature diversity for SAR textures is retained while parameters and FLOPs are reduced. revision: yes

  3. Referee: Experiments: No ablation studies compare Gram polynomials to standard KAN activations or to baseline ResNet, and no details on how VGG16 was trained/adapted on the 1024×1024 resized MSTAR data are supplied, making the reported 163.78× parameter reduction difficult to interpret.

    Authors: We will expand Section 4 to include two new ablation studies: (i) Gram polynomials versus standard KAN activations (B-splines) on MSTAR, and (ii) Light-ResKAN versus the unmodified ResNet baseline. We will also supply explicit implementation details for the VGG16 baseline, including the exact training schedule, adaptation to 1024×1024 inputs, and the precise method used to compute parameter and FLOP counts, ensuring the efficiency ratios are fully reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical architecture validated by direct measurements

full rationale

The paper introduces Light-ResKAN as a ResNet variant that substitutes standard convolutions with KAN convolutions using Gram-polynomial activations and per-channel parameter sharing. All central claims (99.09% MSTAR accuracy, 82.90× FLOPs reduction vs. VGG16, etc.) are presented as measured experimental outcomes on fixed datasets rather than as predictions or theorems derived from the model equations. No equation is shown to equal its own fitted inputs by construction, no uniqueness theorem is invoked via self-citation, and the efficiency numbers are obtained by direct counting of parameters and operations on the implemented network. The derivation chain therefore remains self-contained and non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The design rests on standard neural-network training assumptions plus two paper-specific choices: suitability of Gram polynomials for SAR non-linearities and the claim that channel-wise sharing preserves unique features.

free parameters (2)
  • Gram polynomial degree
    Degree of the polynomial basis used inside each KAN activation; must be chosen or tuned.
  • Architecture depth and width
    Number of residual blocks and channel counts are selected to balance accuracy and cost.
axioms (2)
  • domain assumption KAN layers with learnable activations can achieve comparable or better function approximation than fixed-activation CNNs with fewer parameters
    Invoked when replacing ResNet convolutions with KAN convolutions.
  • ad hoc to paper Gram polynomials are well-suited to capture complex non-linear relationships in SAR imagery
    Stated directly in the abstract as motivation for the activation choice.

pith-pipeline@v0.9.0 · 5567 in / 1444 out tokens · 39648 ms · 2026-05-13T22:17:57.346438+00:00 · methodology

discussion (0)

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