  Symbolic regression (SR) aims to discover concise closed-form mathematical
equations from data, a task fundamental to scientific discovery. However, the
problem is highly challenging because closed-form equations lie in a complex
combinatorial search space. Existing methods, ranging from heuristic search to
reinforcement learning, fail to scale with the number of input variables. We
make the observation that closed-form equations often have structural
characteristics and invariances (e.g., the commutative law) that could be
further exploited to build more effective symbolic regression solutions.
Motivated by this observation, our key contribution is to leverage pre-trained
deep generative models to capture the intrinsic regularities of equations,
thereby providing a solid foundation for subsequent optimization steps. We show
that our novel formalism unifies several prominent approaches of symbolic
regression and offers a new perspective to justify and improve on the previous
ad hoc designs, such as the usage of cross-entropy loss during pre-training.
Specifically, we propose an instantiation of our framework, Deep Generative
Symbolic Regression (DGSR). In our experiments, we show that DGSR achieves a
higher recovery rate of true equations in the setting of a larger number of
input variables, and it is more computationally efficient at inference time
than state-of-the-art RL symbolic regression solutions.
