# Complex Equation Learner: Rational Symbolic Regression with Gradient Descent in Complex Domain

arXiv: https://arxiv.org/abs/2605.03841 · HTML: https://mlsanity.com/paper/2605.03841/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 10 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)

## Abstract (arXiv)

Symbolic regression aims to discover interpretable equations from data, yet modern gradient-based methods fail for operators that introduce singularities or domain constraints, including division, logarithms, and square roots. As a result, Equation Learner-type models typically avoid these operators or impose restrictions, e.g. constraining denominators to prevent poles, which narrows the hypothesis class. We propose a complex weight extension of the Equation Learner that mitigates real-valued optimization pathologies by allowing optimization trajectories to bypass real-axis degeneracies. The proposed approach converges stably even when the target expression has real-domain poles, and it enables unconstrained use of operations such as logarithm and square root. We Validate the method on symbolic regression benchmarks and show it can recover singular behavior from experimental frequency response data.