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FactorLibrary: From Polynomials to Circuits via Recursive Subgoals

arXiv 2606.25394 ↗First posted 24 Jun 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

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%.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 28 references that are in the map. First posted on arXiv 24 Jun 2026.

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References · 11

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  3. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
  4. 2023LeanDojo: Theorem Proving with Retrieval-Augmented Language Modelscited by 427
  5. 2016Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivationcited by 286
  6. 2017Automatic Goal Generation for Reinforcement Learning Agentscited by 259
  7. 2017Thinking Fast and Slow with Deep Learning and Tree Searchcited by 252
  8. 2024DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Searchcited by 197
  9. 2019Soft Actor-Critic for Discrete Action Settingscited by 174
  10. 2020DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learningcited by 161
  11. 2026CircuitBuilder: From Polynomials to Circuits via Reinforcement Learningcited by 1

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