In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks

TL;DR

This paper introduces in-context symbolic regression methods for Kolmogorov-Arnold Networks to improve robustness and accuracy in extracting symbolic formulas, outperforming traditional approaches.

Contribution

It presents two novel in-context symbolic regression techniques, GSR and GMP, that enhance robustness and accuracy in symbolic extraction from KANs.

Findings

GSR achieves up to 99.8% reduction in median OFAT test MSE.

Methods improve robustness and consistency of symbolic formulas.

Experimental results demonstrate superior performance over standard approaches.

Abstract

Symbolic regression aims to replace black-box predictors with concise analytical expressions that can be inspected and validated in scientific machine learning. Kolmogorov-Arnold Networks (KANs) are well suited to this goal because each connection between adjacent units (an "edge") is parametrised by a learnable univariate function that can, in principle, be replaced by a symbolic operator. In practice, however, symbolic extraction is a bottleneck: the standard KAN-to-symbol approach fits operators to each learned edge function in isolation, making the discrete choice sensitive to initialisation and non-convex parameter fitting, and ignoring how local substitutions interact through the full network. We study in-context symbolic regression for operator extraction in KANs, and present two complementary instantiations. Greedy in-context Symbolic Regression (GSR) performs greedy, in-context selection by choosing edge replacements according to end-to-end loss improvement after brief fine-tuning. Gated Matching Pursuit (GMP) amortises this in-context selection by training a differentiable gated operator layer that places an operator library behind sparse gates on each edge; after convergence, gates are discretised (optionally followed by a short in-context greedy refinement pass). We quantify robustness via one-factor-at-a-time (OFAT) hyper-parameter sweeps and assess both predictive error and qualitative consistency of recovered formulas. Across several experiments, greedy in-context symbolic regression achieves up to 99.8% reduction in median OFAT test MSE.