FactorLibrary: From Polynomials to Circuits via Recursive Subgoals
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Computer Science > Machine Learning
Title:FactorLibrary: From Polynomials to Circuits via Recursive Subgoals
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 $91.8\%$.
| Comments: | 14 pages, 8 figures, in 3rd AI for Math Workshop (ICML 2026) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.25394 [cs.LG] |
| (or arXiv:2606.25394v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.25394
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Michael Ruofan Zeng [view email][v1] Wed, 24 Jun 2026 04:45:09 UTC (2,701 KB)
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