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

• URL: http://arxiv.org/abs/2605.03841v1
• Date: Tue, 05 May 2026 15:08:08 GMT
• Title: Complex Equation Learner: Rational Symbolic Regression with Gradient Descent in Complex Domain
• Abstract summary: We propose a complex weight extension of the Equation to mitigate real-valued optimization pathologies.<n>We show it can recover singular behavior from experimental frequency response data.
• Score: 14.570449305774309
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Equation Recast for Canonical Operator Learning Across Parametric PDEs [59.44573033543284]
  We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator.<n>In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries.
  arXiv  Detail & Related papers  (2026-09-02T13:15:50Z)
• Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration [4.389213808289583]
  We develop a sparse framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.<n>SORT estimates expansion coefficients using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation.<n>The central application is data-driven discovery of ordinary differential equations.
  arXiv  Detail & Related papers  (2026-08-13T17:31:27Z)
• Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback [56.69850045068714]
  We introduce textitInfluence-Guided Regression (IGSR), a method that frames equation discovery as an iterative two-step process.<n>We demonstrate IGSRs effectiveness on a diverse suite of benchmarks, including LLM-SRBench, pharmacological PKPD models, an epidemiological simulation, and real-world genomic data.
  arXiv  Detail & Related papers  (2026-05-27T23:48:01Z)
• Data-Efficient Symbolic Regression via Foundation Model Distillation [34.0701397977874]
  EQUATE is a framework that adapts foundation models for symbolic equation discovery in low-data regimes via distillation.<n>It consistently outperforms state-of-the-art baselines in both accuracy and robustness.<n>These results highlight EQUATE as a practical and generalizable solution for data-efficient symbolic regression.
  arXiv  Detail & Related papers  (2025-08-27T00:18:48Z)
• Semi-parametric Functional Classification via Path Signatures Logistic Regression [1.210026603224224]
  We propose Path Signatures Logistic Regression, a semi-parametric framework for classifying vector-valued functional data.<n>Our results highlight the practical and theoretical benefits of integrating rough path theory into modern functional data analysis.
  arXiv  Detail & Related papers  (2025-07-09T08:06:50Z)
• Optimal lower bounds for logistic log-likelihoods [1.3124513975412255]
  The logit transform is arguably the most widely-employed link function beyond linear settings. It is still unclear whether tangent lower bounds sharper than quadratic ones can be derived without undermining the tractability of the resulting minorizer. This article addresses such a challenging question through the design and study of a novel piece-wise quadratic lower bound.
  arXiv  Detail & Related papers  (2024-10-14T09:09:33Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Deep Generative Symbolic Regression [83.04219479605801]
  Symbolic regression aims to discover concise closed-form mathematical equations from data. Existing methods, ranging from search to reinforcement learning, fail to scale with the number of input variables. We propose an instantiation of our framework, Deep Generative Symbolic Regression.
  arXiv  Detail & Related papers  (2023-12-30T17:05:31Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Learning Functional Transduction [9.926231893220063]
  We show that transductive regression principles can be meta-learned through gradient descent to form efficient in-context neural approximators. We demonstrate the benefit of our meta-learned transductive approach to model complex physical systems influenced by varying external factors with little data.
  arXiv  Detail & Related papers  (2023-02-01T09:14:28Z)
• Neural Symbolic Regression that Scales [58.45115548924735]
  We introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs.
  arXiv  Detail & Related papers  (2021-06-11T14:35:22Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.