Data-Efficient Symbolic Regression via Foundation Model Distillation

• URL: http://arxiv.org/abs/2508.19487v1
• Date: Wed, 27 Aug 2025 00:18:48 GMT
• Title: Data-Efficient Symbolic Regression via Foundation Model Distillation
• Authors: Wangyang Ying, Jinghan Zhang, Haoyue Bai, Nanxu Gong, Xinyuan Wang, Kunpeng Liu, Chandan K. Reddy, Yanjie Fu,
• Abstract summary: 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.
• Score: 34.0701397977874
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Discovering interpretable mathematical equations from observed data (a.k.a. equation discovery or symbolic regression) is a cornerstone of scientific discovery, enabling transparent modeling of physical, biological, and economic systems. While foundation models pre-trained on large-scale equation datasets offer a promising starting point, they often suffer from negative transfer and poor generalization when applied to small, domain-specific datasets. In this paper, we introduce EQUATE (Equation Generation via QUality-Aligned Transfer Embeddings), a data-efficient fine-tuning framework that adapts foundation models for symbolic equation discovery in low-data regimes via distillation. EQUATE combines symbolic-numeric alignment with evaluator-guided embedding optimization, enabling a principled embedding-search-generation paradigm. Our approach reformulates discrete equation search as a continuous optimization task in a shared embedding space, guided by data-equation fitness and simplicity. Experiments across three standard public benchmarks (Feynman, Strogatz, and black-box datasets) demonstrate that EQUATE consistently outperforms state-of-the-art baselines in both accuracy and robustness, while preserving low complexity and fast inference. These results highlight EQUATE as a practical and generalizable solution for data-efficient symbolic regression in foundation model distillation settings.

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