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arXiv · 2606.25394

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
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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 $91.8\%$.

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Rohan Pandey, Michael Ruofan Zeng, Weikun K. Zhang, Kaijie Jin, Naomi Morato, Archit Ganapule, Bhaumik Mehta, Jarod Alper. 2026-06-24. FactorLibrary: From Polynomials to Circuits via Recursive Subgoals. https://arxiv.org/abs/2606.25394

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