CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning

Weikun Zhang, Rohan Pandey, Bhaumik Mehta, Kaijie Jin, Naomi Morato, Archit Ganapule, Michael Ruofan Zeng, Jarod Alper

Keywords: reinforcement learning, arithmetic circuits, proximal policy optimization, monte carlo tree search, soft actor-critic, algebraic complexity theory

TL;DR: Reinforcement learning to search for efficient arithmetic circuits

Abstract: Motivated by auto-proof generation and Valiant's VP vs. VNP conjecture, we study the problem of discovering efficient arithmetic circuits to compute polynomials, using addition and multiplication gates. We formulate this problem as a single-player game, where an RL agent attempts to build the circuit within a fixed number of operations. We implement an AlphaZero-style training loop and compare two approaches: Proximal Policy Optimization with Monte Carlo Tree Search (PPO+MCTS) and Soft Actor-Critic (SAC). SAC achieves the highest success rates on two-variable targets, while PPO+MCTS scales to three variables and demonstrates steady improvement on harder instances. These results suggest that polynomial circuit synthesis is a compact, verifiable setting for studying self-improving search policies.

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Submission Number: 107