Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.15250v1</id>\n    <title>In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks</title>\n    <updated>2026-03-16T13:21:26Z</updated>\n    <link href='https://arxiv.org/abs/2603.15250v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.15250v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>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.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n    <published>2026-03-16T13:21:26Z</published>\n    <arxiv:comment>24 pages; Accepted for publication at XAI'2026</arxiv:comment>\n    <arxiv:primary_category term='cs.LG'/>\n    <author>\n      <name>Francesco Sovrano</name>\n    </author>\n    <author>\n      <name>Lidia Losavio</name>\n    </author>\n    <author>\n      <name>Giulia Vilone</name>\n    </author>\n    <author>\n      <name>Marc Langheinrich</name>\n    </author>\n  </entry>"
}