Noise-Resilient Symbolic Regression with Dynamic Gating Reinforcement Learning

2025-01-02

AI Summary

Symbolic regression suffers significant performance degradation under high-noise conditions. Method: This paper proposes a noise-robust reinforcement learning framework featuring a novel Noise-Robust Gating Module (NGM) that dynamically suppresses input noise, and a Mixed-Path Entropy (MPE) reward mechanism that balances exploration and interpretability during expression tree search. The framework integrates dynamic gating, symbolic tree-structured modeling, and entropy regularization to jointly optimize accuracy and robustness. Contribution/Results: Experiments demonstrate that the method substantially outperforms state-of-the-art symbolic regression approaches on high-noise benchmarks. Moreover, it achieves new state-of-the-art performance on clean datasets, confirming its strong generalization capability and adaptability across diverse signal-to-noise ratio regimes.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Symbolic regression (SR) has emerged as a pivotal technique for uncovering the intrinsic information within data and enhancing the interpretability of AI models. However, current state-of-the-art (sota) SR methods struggle to perform correct recovery of symbolic expressions from high-noise data. To address this issue, we introduce a novel noise-resilient SR (NRSR) method capable of recovering expressions from high-noise data. Our method leverages a novel reinforcement learning (RL) approach in conjunction with a designed noise-resilient gating module (NGM) to learn symbolic selection policies. The gating module can dynamically filter the meaningless information from high-noise data, thereby demonstrating a high noise-resilient capability for the SR process. And we also design a mixed path entropy (MPE) bonus term in the RL process to increase the exploration capabilities of the policy. Experimental results demonstrate that our method significantly outperforms several popular baselines on benchmarks with high-noise data. Furthermore, our method also can achieve sota performance on benchmarks with clean data, showcasing its robustness and efficacy in SR tasks.

Problem

• Noisy Data
• Symbolic Regression
• Mathematical Formula Identification

Innovation

• Noise-Resistant Symbolic Regression
• Reinforcement Learning
• Filtering and Reward System