# Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients

arXiv: https://arxiv.org/abs/2406.06751 · HTML: https://mlsanity.com/paper/2406.06751/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 59 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [Interpretable and logic-guided RL](https://mlsanity.com/deeprl/interpretable-and-logic-guided-rl/)

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [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)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (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)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data](https://mlsanity.com/paper/2309.13705/) (2023)
- [DCT-Former: Efficient Self-Attention with Discrete Cosine Transform](https://mlsanity.com/paper/2203.01178/) (2022)
- [Automated Learning of Interpretable Models with Quantified Uncertainty](https://mlsanity.com/paper/2205.01626/) (2022)
- [Vertical Symbolic Regression via Deep Policy Gradient](https://mlsanity.com/paper/2402.00254/) (2024)

## Built on by (most cited first, 4 of 4)

- [Analytical Lyapunov Function Discovery: An RL-based Generative Approach](https://mlsanity.com/paper/2502.02014/) (2025)
- [Parsing the Language of Expression: Enhancing Symbolic Regression with Domain-Aware Symbolic Priors](https://mlsanity.com/paper/2503.09592/) (2025)
- [Deep Variational Inference Symbolic Regression](https://mlsanity.com/paper/2605.01067/) (2026)
- [Bayesian Symbolic Regression with Entropic Reinforcement Learning](https://mlsanity.com/paper/2608.09617/) (2026)

## Abstract (arXiv)

We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a data-specific expression generator, without relying on pretrained models or additional search or planning procedures. Despite the success of existing DSR methods, they are built on recurrent neural networks, solely guided by data fitness, and potentially meet tail barriers that can zero out the policy gradient, causing inefficient model updates. To overcome these limitations, we design a decoder-only architecture that performs attention in the frequency domain and introduce a dual-indexed position encoding to conduct layer-wise generation. Second, we propose a Bayesian information criterion (BIC)-based reward function that can automatically adjust the trade-off between expression complexity and data fitness, without the need for explicit manual tuning. Third, we develop a ranking-based weighted policy update method that eliminates the tail barriers and enhances training effectiveness. Extensive benchmarks and systematic experiments demonstrate the advantages of our approach. We have released our implementation at https://github.com/ZakBastiani/CADSR.