# FactorLibrary: From Polynomials to Circuits via Recursive Subgoals

arXiv: https://arxiv.org/abs/2606.25394 · HTML: https://mlsanity.com/paper/2606.25394/

## 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.

## Builds on (most cited first, 11 of 11)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation](https://mlsanity.com/paper/1604.06057/) (2016)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Soft Actor-Critic for Discrete Action Settings](https://mlsanity.com/paper/1910.07207/) (2019)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning](https://mlsanity.com/paper/2603.17075/) (2026)

## 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%.