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

arXiv: https://arxiv.org/abs/2603.15250 · HTML: https://mlsanity.com/paper/2603.15250/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)

## Abstract (arXiv)

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.