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Comparative Evaluation of Kolmogorov-Arnold Autoencoders and Orthogonal Autoencoders for Fault Detection with Varying Training Set Sizes

Enrique Luna Villagómez, Vladimir Mahalec

TL;DR

The paper evaluates Kolmogorov-Arnold Autoencoders (KAN-AEs) for unsupervised fault detection on the Tennessee Eastman Process, comparing four edge-function parameterizations (EfficientKAN, FastKAN, FourierKAN, WavKAN) against an Orthogonal Autoencoder (OAE) across multiple training-set sizes. By training exclusively on normal data, the study assesses data efficiency, fault-type sensitivity, and uses Bayesian signed-rank tests to quantify practical superiority or equivalence. Key findings show that WavKAN-AE achieves strong detection with very limited data, EfficientKAN-AE excels in data-scarce regimes, while FourierKAN underperforms; as data grow, OAE becomes competitive and, in some cases, superior. The results suggest KAN-AEs offer data-efficient, interpretable alternatives for industrial fault monitoring, with future work needed to incorporate temporal modeling and formal interpretability tooling.

Abstract

Kolmogorov-Arnold Networks (KANs) have recently emerged as a flexible and parameter-efficient alternative to conventional neural networks. Unlike standard architectures that use fixed node-based activations, KANs place learnable functions on edges, parameterized by different function families. While they have shown promise in supervised settings, their utility in unsupervised fault detection remains largely unexplored. This study presents a comparative evaluation of KAN-based autoencoders (KAN-AEs) for unsupervised fault detection in chemical processes. We investigate four KAN-AE variants, each based on a different KAN implementation (EfficientKAN, FastKAN, FourierKAN, and WavKAN), and benchmark them against an Orthogonal Autoencoder (OAE) on the Tennessee Eastman Process. Models are trained on normal operating data across 13 training set sizes and evaluated on 21 fault types, using Fault Detection Rate (FDR) as the performance metric. WavKAN-AE achieves the highest overall FDR ($\geq$92\%) using just 4,000 training samples and remains the top performer, even as other variants are trained on larger datasets. EfficientKAN-AE reaches $\geq$90\% FDR with only 500 samples, demonstrating robustness in low-data settings. FastKAN-AE becomes competitive at larger scales ($\geq$50,000 samples), while FourierKAN-AE consistently underperforms. The OAE baseline improves gradually but requires substantially more data to match top KAN-AE performance. These results highlight the ability of KAN-AEs to combine data efficiency with strong fault detection performance. Their use of structured basis functions suggests potential for improved model transparency, making them promising candidates for deployment in data-constrained industrial settings.

Comparative Evaluation of Kolmogorov-Arnold Autoencoders and Orthogonal Autoencoders for Fault Detection with Varying Training Set Sizes

TL;DR

The paper evaluates Kolmogorov-Arnold Autoencoders (KAN-AEs) for unsupervised fault detection on the Tennessee Eastman Process, comparing four edge-function parameterizations (EfficientKAN, FastKAN, FourierKAN, WavKAN) against an Orthogonal Autoencoder (OAE) across multiple training-set sizes. By training exclusively on normal data, the study assesses data efficiency, fault-type sensitivity, and uses Bayesian signed-rank tests to quantify practical superiority or equivalence. Key findings show that WavKAN-AE achieves strong detection with very limited data, EfficientKAN-AE excels in data-scarce regimes, while FourierKAN underperforms; as data grow, OAE becomes competitive and, in some cases, superior. The results suggest KAN-AEs offer data-efficient, interpretable alternatives for industrial fault monitoring, with future work needed to incorporate temporal modeling and formal interpretability tooling.

Abstract

Kolmogorov-Arnold Networks (KANs) have recently emerged as a flexible and parameter-efficient alternative to conventional neural networks. Unlike standard architectures that use fixed node-based activations, KANs place learnable functions on edges, parameterized by different function families. While they have shown promise in supervised settings, their utility in unsupervised fault detection remains largely unexplored. This study presents a comparative evaluation of KAN-based autoencoders (KAN-AEs) for unsupervised fault detection in chemical processes. We investigate four KAN-AE variants, each based on a different KAN implementation (EfficientKAN, FastKAN, FourierKAN, and WavKAN), and benchmark them against an Orthogonal Autoencoder (OAE) on the Tennessee Eastman Process. Models are trained on normal operating data across 13 training set sizes and evaluated on 21 fault types, using Fault Detection Rate (FDR) as the performance metric. WavKAN-AE achieves the highest overall FDR (92\%) using just 4,000 training samples and remains the top performer, even as other variants are trained on larger datasets. EfficientKAN-AE reaches 90\% FDR with only 500 samples, demonstrating robustness in low-data settings. FastKAN-AE becomes competitive at larger scales (50,000 samples), while FourierKAN-AE consistently underperforms. The OAE baseline improves gradually but requires substantially more data to match top KAN-AE performance. These results highlight the ability of KAN-AEs to combine data efficiency with strong fault detection performance. Their use of structured basis functions suggests potential for improved model transparency, making them promising candidates for deployment in data-constrained industrial settings.

Paper Structure

This paper contains 32 sections, 21 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Autoencoders
  4. Kolmogorov-Arnold Networks
  5. KAN Variants
  6. EfficientKAN
  7. FastKAN
  8. FourierKAN
  9. WavKAN
  10. Kolmogorov-Arnold Autoencoder
  11. Methodology
  12. Case Study: The Tennessee Eastman Process
  13. Data Preprocessing
  14. Process Monitoring Models
  15. Training Procedure
  16. ...and 17 more sections

Figures (7)

  • Figure 1: Comparison of (a) MLP-based and (b) KAN-based autoencoders. KAN-based models replace fixed activation functions with learnable univariate transformations along each edge.
  • Figure 2: Tennessee Eastman Process flowsheet.
  • Figure 3: Fault Detection Rate (FDR) across different training sample sizes for controllable faults.
  • Figure 4: Fault Detection Rate (FDR) across different training sample sizes for back-to-control faults.
  • Figure 5: Fault Detection Rate (FDR) across different training sample sizes for uncontrollable faults.
  • ...and 2 more figures