# Improving Neural Symbolic Regression with a Diverse Prior and Post-training Alignment

arXiv: https://arxiv.org/abs/2610.17994 · HTML: https://mlsanity.com/paper/2610.17994/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (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)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [TabICLv2: A better, faster, scalable, and open tabular foundation model](https://mlsanity.com/paper/2602.11139/) (2026)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Scalable-Softmax Is Superior for Attention](https://mlsanity.com/paper/2501.19399/) (2025)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Risk-Sensitive RL for Alleviating Exploration Dilemmas in Large Language Models](https://mlsanity.com/paper/2509.24261/) (2025)
- [Multi-View Symbolic Regression](https://mlsanity.com/paper/2402.04298/) (2024)
- [Towards Scaling Laws for Symbolic Regression](https://mlsanity.com/paper/2510.26064/) (2025)
- [Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression](https://mlsanity.com/paper/2602.08885/) (2026)

## Abstract (arXiv)

Symbolic regression is the problem of finding an expression that fits a dataset. Solving it requires searching a combinatorial space of candidate expressions. Neural symbolic regression can amortize that search by training a model once on synthetic data and then predicting expressions for a new dataset. But existing models still underperform genetic programming on real, noisy data. We argue that the deficit lies in the training rather than in the paradigm, and present RASR (Reinforced Amortized Symbolic Regression), a method with two key changes to the training recipe. First, we design a synthetic prior that narrows the gap with real-world data: inputs come from the prior of a tabular foundation model; constants are sampled bottom-up, conditioned on the data; targets carry heteroscedastic and structured noise; and everything is standardized. Second, we split training into two stages. Supervised pre-training maximizes the token-level likelihood of a reference expression. This is followed by reinforcement-learning post-training that aligns the model with its inference-time use by rewarding held-out fit and penalizing expression size. On the black-box track of SRBench 2.0, RASR achieves the best mean test R2 rank of all evaluated methods. Three RASR variants, trained with different size penalties, make up most of the accuracy-complexity Pareto front. On Strogatz, our method recovers more ground-truth expressions than any baseline, and on Feynman it is competitive with the best-performing methods.