Neural Structure Embedding for Symbolic Regression via Continuous Structure Search and Coefficient Optimization

• URL: http://arxiv.org/abs/2603.22429v1
• Date: Mon, 23 Mar 2026 18:04:03 GMT
• Title: Neural Structure Embedding for Symbolic Regression via Continuous Structure Search and Coefficient Optimization
• Abstract summary: SRCO is a unified embedding-driven framework for symbolic regression.<n>It transforms symbolic structures into a continuous, optimizable representation space.<n> Experiments on synthetic and real-world datasets show that our approach consistently outperforms state-of-the-art methods in equation accuracy, robustness, and search efficiency.
• Score: 8.496933324334167
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational cost, unstable performance, and limited scalability to large equation spaces. To address these challenges, we propose SRCO, a unified embedding-driven framework for symbolic regression that transforms symbolic structures into a continuous, optimizable representation space. The framework consists of three key components: (1) structure embedding: we first generate a large pool of exploratory equations using traditional symbolic regression algorithms and train a Transformer model to compress symbolic structures into a continuous embedding space; (2) continuous structure search: the embedding space enables efficient exploration using gradient-based or sampling-based optimization, significantly reducing the cost of navigating the combinatorial structure space; and (3) coefficient optimization: for each discovered structure, we treat symbolic coefficients as learnable parameters and apply gradient optimization to obtain accurate numerical values. Experiments on synthetic and real-world datasets show that our approach consistently outperforms state-of-the-art methods in equation accuracy, robustness, and search efficiency. This work introduces a new paradigm for symbolic regression by bridging symbolic equation discovery with continuous embedding learning and optimization.

Related papers

• SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery [29.456350389050574]
  Symbolic regression discovers closed-form mathematical expressions from data, offering interpretability beyond black-box models.<n>We introduce SMILE, a hybrid framework that unifies continuous gradient-based optimization with discrete symbolic recovery.<n>We evaluate SMILE on SRBench across ground-truth and black-box datasets, with ablation studies validating each component.
  arXiv  Detail & Related papers  (2026-09-04T02:20:00Z)
• Adaptive Latent Trajectory Anchoring for Action Segmentation Dataset Condensation [53.60856261088647]
  This paper proposes to shift the condensation paradigm from optimization-based inversion to deterministic latent mapping.<n>We represent action segments as continuous trajectories anchored by sparse latent points in the noise manifold.<n>Our framework significantly outperforms state-of-the-art methods in segmentation performance across common datasets.
  arXiv  Detail & Related papers  (2026-07-10T04:00:26Z)
• When Good Equations Get Bad Scores: Improving Symbolic Regression Through Better Parameter Optimization [24.34939435234426]
  Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data.<n>We propose SAGE-Fit, an SR fitting framework that exploits the dual priors of symbolic expressions.
  arXiv  Detail & Related papers  (2026-05-22T06:23:28Z)
• Graph Neural Network Assisted Genetic Algorithm for Structural Dynamic Response and Parameter Optimization [1.5383027029023142]
  optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c) is critical for designing efficient, resilient, and stable structures.<n>This study proposes a hybrid data-driven framework that integrates a Graph Neural Network (GNN) surrogate model with a Genetic Algorithm (GA) to overcome these challenges.
  arXiv  Detail & Related papers  (2025-10-26T21:14:59Z)
• LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data [51.47827479376251]
  LOCAL is a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures.<n>Asymptotic Causal Learning Mask (ACML) and Dynamic Graph Learning (DGPL)<n>Experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods.
  arXiv  Detail & Related papers  (2024-10-25T10:48:41Z)
• A Practical Solver for Scalar Data Topological Simplification [7.079737824450954]
  This paper presents a practical approach for the optimization of topological simplification. We show that our approach leads to improvements over standard topological techniques for removing filament loops. We also show how our approach can be used to repair genus defects in surface processing.
  arXiv  Detail & Related papers  (2024-07-17T08:25:32Z)
• 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)
• Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization [71.69092462147292]
  Performance embeddings enable knowledge transfer of performance tuning between applications. We demonstrate this transfer tuning approach on case studies in deep neural networks, dense and sparse linear algebra compositions, and numerical weather prediction stencils.
  arXiv  Detail & Related papers  (2023-03-14T15:51:35Z)
• Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces [54.58348769621782]
  Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
  arXiv  Detail & Related papers  (2022-07-02T16:59:37Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication [2.055204980188575]
  Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions.
  arXiv  Detail & Related papers  (2021-09-28T17:47:51Z)

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.