FactorLibrary: From Polynomials to Circuits via Recursive Subgoals
Rohan Pandey, Michael Ruofan Zeng, Weikun K. Zhang, Kaijie Jin, Naomi Morato, Archit Ganapule, Bhaumik Mehta, Jarod Alper
Abstract
Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory. We formulate it as a reinforcement learning problem in two directions, bottom-up and top-down. To address the challenge of a fast-growing combinatorial search space, we introduce FactorLibrary, which stores factorizable subexpressions that serve as reusable subgoals across training episodes. We trained a bottom-up agent with Gumbel-PPO-MCTS and two top-down agents with PPO+MCTS and SAC. The PPO+MCTS top-down agent exhibited the most stable performance, finding certified optimal circuits up to complexity $8$ with a success rate of $91.8\%$.
Topics
Classified with taxonomy v2 on Wed, 2 Sept 2026.