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

We propose a novel deep symbolic regression (DSR) approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Existing DSR methods 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 address these issues, 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.