Complex Equation Learner: Rational Symbolic Regression with Gradient Descent in Complex Domain
For researchers using symbolic regression, this work addresses the limitation of gradient-based methods in handling operators with singularities, enabling a broader class of interpretable equations.
The paper proposes a complex weight extension of the Equation Learner that enables stable gradient-based symbolic regression with operators like division, logarithm, and square root, even when target expressions have real-domain poles. The method recovers singular behavior from experimental frequency response data.
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.