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ER-KANs Boost Robustness in Scientific Machine Learning

Harshil Lodhiya· August 18, 2026 View original

Key takeaways

  • ER-KANs are a new KAN variant designed for noisy, data-scarce scientific ML.
  • They achieve significantly higher robustness to noise than other KANs and MLPs.
  • Key features include shared Gaussian RBF bases, curriculum noise injection, and adaptive regularization.
  • ER-KANs offer improved accuracy and reliability in challenging data environments.

Who benefits

Scientific ResearchHealthcareMaterials ScienceAerospaceEnvironmental Monitoring

Summary

Researchers introduce ER-KANs (Efficient and Robust Kolmogorov-Arnold Networks), a new variant designed for data-scarce and noisy scientific machine learning settings. ER-KANs achieve significantly higher robustness to noise compared to other KAN variants and standard MLPs, combining shared Gaussian RBF bases, curriculum noise injection, and entropy-weighted adaptive regularization to maintain accuracy even with corrupted training data.

A new variant of Kolmogorov-Arnold Networks (KANs), termed ER-KANs (Efficient and Robust KANs), has been developed specifically to address challenges in scientific machine learning characterized by limited and noisy data. Existing efficient KANs often perform poorly when data is corrupted, a critical limitation in many real-world scientific applications. ER-KANs incorporate three key design principles to enhance robustness: shared Gaussian Radial Basis Function (RBF) bases across layers for efficient parameterization and locality, curriculum noise injection during training to explicitly teach noise resilience, and entropy-weighted adaptive regularization to prevent overfitting, particularly with small datasets. Evaluations demonstrate that ER-KANs significantly outperform other KAN variants and standard Multi-Layer Perceptrons (MLPs) in noisy environments. For instance, while other KANs saw a 7.9x to 10.6x increase in test MSE with noise, ER-KANs only experienced a 1.4x increase. This robust performance was observed across various analytic functions and in physics-informed neural network (PINN) applications, making them highly suitable for data-scarce scientific modeling.

Why it matters

Professionals in scientific research, engineering, and data science can leverage ER-KANs to build more reliable and accurate machine learning models, especially when working with inherently noisy or limited experimental data, reducing the need for extensive data cleaning or collection.

How to implement this in your domain

  1. 1Evaluate current machine learning models used for scientific data, especially those struggling with noise or data scarcity.
  2. 2Explore replacing existing neural network architectures with ER-KANs for specific modeling tasks.
  3. 3Implement the ER-KAN design choices, including shared Gaussian RBF bases and curriculum noise injection, in your model training.
  4. 4Apply entropy-weighted adaptive regularization to prevent overfitting when working with small datasets.
  5. 5Benchmark ER-KANs against your current models using noisy, data-scarce datasets to quantify performance improvements.

Original post by Harshil Lodhiya

"arXiv:2608.14773v1 Announce Type: new Abstract: The efficient-KAN literature---covering Chebyshev, wavelet, and radial-basis-function variants of the original Kolmogorov-Arnold Network---has been benchmarked almost entirely on clean data. We show that this choice conceals a large…"

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Originally posted by Harshil Lodhiya on X · view source

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