用扩散模型生成高质量数学公式，提升符号回归效果。
Diffusion-Based Symbolic Regression
- 基于随机掩码构建扩散过程，生成多样方程
- 结合强化学习优化，显著提升公式拟合精度
- 适合需要自动发现物理规律的研究者
扩散模型在图像与音频生成中表现卓越。受此启发，我们提出一种新的基于扩散的符号回归方法。通过构建基于随机掩码的扩散与去噪过程，生成多样且高质量的数学表达式。将该生成过程与逐标记的组相对策略优化（GRPO）相结合，在给定测量数据集上实现高效的强化学习。此外，引入长短期风险偏好策略，扩大表现最优候选公式池，进一步提升性能。大量实验与消融研究验证了该方法的有效性。
原文摘要 · Abstract (English)
Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic regression. We construct a random mask-based diffusion and denoising process to generate diverse and high-quality equations. We integrate this generative processes with a token-wise Group Relative Policy Optimization (GRPO) method to conduct efficient reinforcement learning on the given measurement dataset. In addition, we introduce a long short-term risk-seeking policy to expand the pool of top-performing candidates, further enhancing performance. Extensive experiments and ablation studies have demonstrated the effectiveness of our approach.
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