# Data-Efficient Symbolic Regression via Foundation Model Distillation

arXiv: https://arxiv.org/abs/2508.19487 · HTML: https://mlsanity.com/paper/2508.19487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Sequence-to-Sequence Learning as Beam-Search Optimization](https://mlsanity.com/paper/1606.02960/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Self-optimizing Feature Generation via Categorical Hashing Representation and Hierarchical Reinforcement Crossing](https://mlsanity.com/paper/2309.04612/) (2023)
- [Deep Learning and Symbolic Regression for Discovering Parametric Equations](https://mlsanity.com/paper/2207.00529/) (2022)
- [Feature Selection as Deep Sequential Generative Learning](https://mlsanity.com/paper/2403.03838/) (2024)
- [Unsupervised Generative Feature Transformation via Graph Contrastive Pre-training and Multi-objective Fine-tuning](https://mlsanity.com/paper/2405.16879/) (2024)
- [CT-PatchTST: Channel-Time Patch Time-Series Transformer for Long-Term Renewable Energy Forecasting](https://mlsanity.com/paper/2501.08620/) (2025)
- [Reinforcement Feature Transformation for Polymer Property Performance Prediction](https://mlsanity.com/paper/2409.15616/) (2024)
- [Revolutionizing Biomarker Discovery: Leveraging Generative AI for Bio-Knowledge-Embedded Continuous Space Exploration](https://mlsanity.com/paper/2409.15612/) (2024)
- [Topology-aware Reinforcement Feature Space Reconstruction for Graph Data](https://mlsanity.com/paper/2411.05742/) (2024)
- [Image-to-Image Translation with Diffusion Transformers and CLIP-Based Image Conditioning](https://mlsanity.com/paper/2505.16001/) (2025)
- [Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback](https://mlsanity.com/paper/2505.15572/) (2025)

## Built on by (most cited first, 1 of 1)

- [Multi-Agent Procedural Graph Extraction with Structural and Logical Refinement](https://mlsanity.com/paper/2601.19170/) (2026)

## Abstract (arXiv)

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.