CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning
arXiv:2603.17075v1 Announce Type: new Abstract: Motivated by auto-proof generation and Valiant's VP vs. VNP conjecture, we study the problem of discovering efficient arithmetic circuits to compute polynomials, using addition and multiplication gates. We formulate this problem as a single-player game, where an RL agent attempts to build the circuit within a fixed number of operations. We implement an AlphaZero-style training loop and compare two approaches: Proximal Policy Optimization with Monte Carlo Tree Search (PPO+MCTS) and Soft Actor-Critic (SAC). SAC achieves the highest success rates on two-variable targets, while PPO+MCTS scales to three variables and demonstrates steady improvement on harder instances. These results suggest that polynomial circuit synthesis is a compact, verifiable setting for studying self-improving search policies.
arXiv:2603.17075v1 Announce Type: new Abstract: Motivated by auto-proof generation and Valiant's VP vs. VNP conjecture, we study the problem of discovering efficient arithmetic circuits to compute polynomials, using addition and multiplication gates. We formulate this problem as a single-player game, where an RL agent attempts to build the circuit within a fixed number of operations. We implement an AlphaZero-style training loop and compare two approaches: Proximal Policy Optimization with Monte Carlo Tree Search (PPO+MCTS) and Soft Actor-Critic (SAC). SAC achieves the highest success rates on two-variable targets, while PPO+MCTS scales to three variables and demonstrates steady improvement on harder instances. These results suggest that polynomial circuit synthesis is a compact, verifiable setting for studying self-improving search policies.
Executive Summary
The article presents CircuitBuilder, a reinforcement learning framework for discovering efficient arithmetic circuits to compute polynomials using addition and multiplication gates. Building upon the work of Valiant's VP vs. VNP conjecture, the authors formulate the problem as a single-player game and implement two RL approaches: Proximal Policy Optimization with Monte Carlo Tree Search (PPO+MCTS) and Soft Actor-Critic (SAC). The results demonstrate the effectiveness of SAC on two-variable targets and PPO+MCTS on three variables. This work contributes to the study of self-improving search policies and has implications for auto-proof generation and circuit synthesis. The findings suggest that polynomial circuit synthesis is a compact and verifiable setting for studying RL policies. While the study demonstrates promising results, the generalizability of the findings to more complex circuits and real-world applications is uncertain.
Key Points
- ▸ CircuitBuilder is a reinforcement learning framework for discovering efficient arithmetic circuits.
- ▸ The framework uses addition and multiplication gates to compute polynomials.
- ▸ Proximal Policy Optimization with Monte Carlo Tree Search (PPO+MCTS) and Soft Actor-Critic (SAC) are implemented as RL approaches.
Merits
Strength in RL Policy Evaluation
CircuitBuilder provides a compact and verifiable setting for studying self-improving search policies, contributing to the evaluation of RL policies in a controlled environment.
Demerits
Limited Generalizability
The study's findings are uncertain in terms of generalizability to more complex circuits and real-world applications, limiting the practical implications of the research.
Expert Commentary
The CircuitBuilder framework demonstrates the potential of reinforcement learning for discovering efficient arithmetic circuits. While the study's findings are promising, the generalizability of the results to more complex circuits and real-world applications is uncertain. Further research is needed to explore the limitations and potential extensions of the framework. Additionally, the study's contribution to the evaluation of RL policies in a controlled environment is a significant strength. Nevertheless, the practical implications of the research are uncertain, and the development of more efficient auto-proof generation and circuit synthesis techniques remains an open challenge.
Recommendations
- ✓ Future research should focus on exploring the generalizability of the CircuitBuilder framework to more complex circuits and real-world applications.
- ✓ The development of more efficient RL policies using the CircuitBuilder framework should be pursued to improve the practical implications of the research.
