arXiv:2606.25394v1 Announce Type: new 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-
The increasing complexity of AI tasks and the need for more efficient computational methods are driving research into novel problem-solving approaches like reinforcement learning for algebraic problems.
This research addresses a fundamental computational challenge directly applicable to optimizing AI models and potentially accelerating advancements in various scientific and engineering fields.
The proposed FactorLibrary and RL agents offer a new methodology for discovering minimal arithmetic circuits, potentially leading to more efficient computation for complex mathematical problems.
- · AI researchers
- · Algebraic complexity theorists
- · Computational mathematics sector
- · Traditional brute-force optimization methods
More efficient algorithms for complex polynomial factorization are developed.
Improved computational efficiency of machine learning models and large-scale data processing becomes possible.
New classes of AI agents emerge that can autonomously discover and optimize mathematical structures.
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