Evaluating the Effectiveness of SechKAN on 1D Data

A comparative study of hyperbolic secant-based Kolmogorov-Arnold Networks for 1D classification

Hoang-Thang Ta· 2026· DOI 10.48550/arXiv.2609.25876

The core problem

The Kolmogorov-Arnold representation theorem (KART) states that any continuous multivariate function can be represented as a superposition of continuous univariate functions and addition. This theorem has inspired Kolmogorov-Arnold Networks (KANs), which replace fixed activation functions on nodes with learnable activation functions on edges. KANs have shown promise in various domains, from solving STEM problems to AI tasks. However, their parameter efficiency and effectiveness on 1D data remain under-explored. This paper investigates SechKAN, a KAN variant that uses hyperbolic secant (sech) functions as basis functions, combined with a 1D projection to reduce the number of parameters to a level comparable to multilayer perceptrons (MLPs). The study evaluates SechKAN on three 1D classification datasets: UCI Human Activity Recognition (UCI HAR), ElectricDevices, and Crop, and compares it with several effective networks including EfficientKAN, MLP, CNN1D, ResNet1D, and DSCNN1D under approximately comparable parameter budgets. The goal is to assess whether SechKAN can offer competitive performance and to understand the impact of architectural choices such as grid size and normalizatio

SechKAN achieves competitive performance across the three datasets. On UCI HAR, SechKAN performs comparably to MLP and CNN1D, while on ElectricDevices, it shows similar accuracy to ResNet1D and DSCNN1D. Notably, on the Crop dataset, SechKAN outperforms all other models, achieving the highest accuracy. The table below summarizes the accuracy (in percentage) of each model on the three datasets: | Model | UCI HAR | ElectricDevices | Crop | |-------------|---------|-----------------|------| | SechKAN | 95.2 | 84.7 | 92.3 | | EfficientKAN| 94.8 | 83.9 | 90.1 | | MLP | 95.0 | 84.2 | 89.5 | | CNN1D | 95.5 | 85.1 | 90.8 | | ResNet1D | 95.8 | 85.3 | 91.2 | | DSCNN1D | 95.6 | 85.0 | 91.0 | These results indicate that SechKAN is particularly effective on the Crop dataset, where it surpasses the next best model (ResNet1D) by 1.1 percentage points. On the other datasets, the differences are within 1 percentage point, suggesting that SechKAN is a viable alternative to traditional architectures.

The Kolmogorov-Arnold representation theorem (KART) states that any continuous multivariate function can be represented as a superposition of continuous univariate functions and addition. This theorem has inspired Kolmogorov-Arnold Networks (KANs), which replace fixed activation functions on nodes with learnable activation functions on edges. KANs have shown promise in various domains, from solving STEM problems to AI tasks. However, their parameter efficiency and effectiveness on 1D data remain under-explored. This paper investigates SechKAN, a KAN variant that uses hyperbolic secant (sech) functions as basis functions, combined with a 1D projection to reduce the number of parameters to a level comparable to multilayer perceptrons (MLPs). The study evaluates SechKAN on three 1D classification datasets: UCI Human Activity Recognition (UCI HAR), ElectricDevices, and Crop, and compares it with several effective networks including EfficientKAN, MLP, CNN1D, ResNet1D, and DSCNN1D under approximately comparable parameter budgets. The goal is to assess whether SechKAN can offer competitive performance and to understand the impact of architectural choices such as grid size and normalization.

SechKAN is built upon the KAN framework, where each edge in the network computes a learnable univariate function. In SechKAN, these functions are parameterized as a linear combination of hyperbolic secant basis functions:

Ablation studies reveal that the grid size G and normalization significantly affect SechKAN's performance. Increasing the grid size generally improves accuracy up to a point, after which performance plateaus or degrades due to overfitting. Normalization, such as batch normalization or layer normalization, is crucial for stabilizing training and achieving good results. The effectiveness of SechKAN is thus dataset-dependent and influenced by architectural choices. For instance, on Crop, a larger grid size with layer normalization yields the best performance, while on UCI HAR, a smaller grid size with batch normalization is sufficient. These findings suggest that SechKAN's advantages are not universal but can be harnessed with proper tuning. Future work could explore adaptive grid sizes and other basis functions to further enhance performance. The source code and experimental implementation are publicly available at https://github.com/hoangthangta/SechKAN_1D.

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