GENSR: Symbolic Regression Based in Equation Generative Space

• URL: http://arxiv.org/abs/2602.20557v1
• Date: Tue, 24 Feb 2026 05:14:34 GMT
• Title: GENSR: Symbolic Regression Based in Equation Generative Space
• Authors: Qian Li, Yuxiao Hu, Juncheng Liu, Yuntian Chen,
• Abstract summary: GenSR is a generative latent space-based SR framework.<n>From a Bayesian perspective, GenSR reframes the SR task as maximizing the conditional distribution $p(mathrmEqu. mid mathrmNum.)$.
• Score: 15.186848349610363
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space-based SR framework following the `map construction -> coarse localization -> fine search'' paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured `map'' of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the candidate region, leveraging smooth latent gradients. From a Bayesian perspective, GenSR reframes the SR task as maximizing the conditional distribution $p(\mathrm{Equ.} \mid \mathrm{Num.})$, with CVAE training achieving this objective through the Evidence Lower Bound (ELBO). This new perspective provides a theoretical guarantee for the effectiveness of GenSR. Extensive experiments show that GenSR jointly optimizes predictive accuracy, expression simplicity, and computational efficiency, while remaining robust under noise.

Related papers

• SVRecon: Sparse Voxel Rasterization for Surface Reconstruction [60.92372415355283]
  We extend the recently proposed sparse voxelization paradigm to the task of high-fidelity surface reconstruction by integrating SVRecon.<n>Our method achieves strong reconstruction accuracy while having consistently speedy convergence.
  arXiv  Detail & Related papers  (2025-11-21T16:32:01Z)
• Hybrid second-order gradient histogram based global low-rank sparse regression for robust face recognition [4.582941396468189]
  Low-rank regression models have been widely adopted in face recognition due to their robustness against illumination variations.<n>Existing methods often suffer from insufficient feature representation and limited modeling of structured corruption across samples.<n>This paper proposes a Hybrid second-order gradient Histogram based Global Low-Rank Sparse Regression model.
  arXiv  Detail & Related papers  (2025-11-08T07:31:38Z)
• DeSiRe-GS: 4D Street Gaussians for Static-Dynamic Decomposition and Surface Reconstruction for Urban Driving Scenes [71.61083731844282]
  We present DeSiRe-GS, a self-supervised gaussian splatting representation.<n>It enables effective static-dynamic decomposition and high-fidelity surface reconstruction in complex driving scenarios.
  arXiv  Detail & Related papers  (2024-11-18T05:49:16Z)
• Accelerating Distributed Stochastic Optimization via Self-Repellent Random Walks [11.3631620309434]
  We study a family of distributed optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. We take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW) We prove that the optimization errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem.
  arXiv  Detail & Related papers  (2024-01-18T00:50:37Z)
• 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)
• GFN-SR: Symbolic Regression with Generative Flow Networks [0.9208007322096533]
  In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field. We propose an alternative framework (GFN-SR) to approach SR with deep learning. GFN-SR is capable of generating a diverse set of best-fitting expressions.
  arXiv  Detail & Related papers  (2023-12-01T07:38:05Z)
• Sparse-Inductive Generative Adversarial Hashing for Nearest Neighbor Search [8.020530603813416]
  We propose a novel unsupervised hashing method, termed Sparsity-Induced Generative Adversarial Hashing (SiGAH) SiGAH encodes large-scale high-scale high-dimensional features into binary codes, which solves the two problems through a generative adversarial training framework. Experimental results on four benchmarks, i.e. Tiny100K, GIST1M, Deep1M, and MNIST, have shown that the proposed SiGAH has superior performance over state-of-the-art approaches.
  arXiv  Detail & Related papers  (2023-06-12T08:07:23Z)
• Efficient Generator of Mathematical Expressions for Symbolic Regression [0.0]
  We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.
  arXiv  Detail & Related papers  (2023-02-20T10:40:29Z)
• NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer [45.47667026025716]
  We propose a novel, robust and accelerated iteration that relies on two key elements. The convergence and stability of the obtained method, referred to as NAG-GS, are first studied extensively. We show that NAG-arity is competitive with state-the-art methods such as momentum SGD with weight decay and AdamW for the training of machine learning models.
  arXiv  Detail & Related papers  (2022-09-29T16:54:53Z)
• On the Double Descent of Random Features Models Trained with SGD [78.0918823643911]
  We study properties of random features (RF) regression in high dimensions optimized by gradient descent (SGD) We derive precise non-asymptotic error bounds of RF regression under both constant and adaptive step-size SGD setting. We observe the double descent phenomenon both theoretically and empirically.
  arXiv  Detail & Related papers  (2021-10-13T17:47:39Z)
• Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling? [59.820507600960745]
  We propose a new GCP meta-layer that uses SVD in the forward pass, and Pad'e Approximants in the backward propagation to compute the gradients. The proposed meta-layer has been integrated into different CNN models and achieves state-of-the-art performances on both large-scale and fine-grained datasets.
  arXiv  Detail & Related papers  (2021-05-06T08:03:45Z)
• Making Affine Correspondences Work in Camera Geometry Computation [62.7633180470428]
  Local features provide region-to-region rather than point-to-point correspondences. We propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. Experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times.
  arXiv  Detail & Related papers  (2020-07-20T12:07:48Z)

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.