In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914484637925376 |
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| author | Sovrano, Francesco Losavio, Lidia Vilone, Giulia Langheinrich, Marc |
| author_facet | Sovrano, Francesco Losavio, Lidia Vilone, Giulia Langheinrich, Marc |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15250 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks Sovrano, Francesco Losavio, Lidia Vilone, Giulia Langheinrich, Marc Machine Learning Artificial Intelligence 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. |
| title | In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.15250 |