Enhancing Deep Symbolic Regression via Reasoning Equivalent Expressions

Nan Jiang, Ziyi Wang, Yexiang Xue

Keywords: symbolic regression, deep reinforcement learning, symbolic reasoning

TL;DR: We introduce a deep reinforcement learning approach for symbolic regression that reduces the instability of policy gradients by using numerically equivalent but symbolically distinct expressions.

Abstract:

Symbolic regression seeks to uncover physical knowledge from experimental data. Recently a line of work on deep reinforcement learning (DRL) formulated the search for optimal expressions as a sequential decision-making problem. However, training these models is challenging due to the inherent instability of the policy gradient estimator.
We observe that many numerically equivalent yet symbolically distinct expressions exist, such as $\log(x_1^2 x_2^3)$ and $2\log(x_1) + 3\log(x_2)$.
Building on this, we propose Deep Symbolic Regression via Reasoning Equivalent eXpressions (DSR-Rex). The high-level idea is to enhance policy gradient estimation by leveraging both expressions sampled from the DRL and their numerically identical counterparts generated via an expression reasoning module.
Our DSR-Rex (1) embeds mathematical laws and equalities into the deep model, (2) reduces gradient estimator variance with theoretical justification and (3) encourages RL exploration of different symbolic forms in the search space of all expressions.
In our experiments, DSR-Rex is evaluated on several challenging scientific datasets, demonstrating superior performance in discovering equations with lower Normalized MSE scores. Additionally, DSR-Rex computes gradients with smaller empirical standard deviation, compared to the previous DSR method.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 5648