CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning

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.

Demonstrating Wheeled Lab: Modern Sim2Real for Low-cost, Open-source Wheeled Robotics

Simulation has been pivotal in recent robotics milestones and is poised to play a prominent role in the field's future. However, recent robotic advances often rely on expensive and high-maintenance platforms, limiting access to broader robotics audiences. This work introduces Wheeled Lab, a framework for the low-cost, open-source wheeled platforms that are already widely established in education and research. Through integration with Isaac Lab, Wheeled Lab introduces modern techniques in Sim2Real, such as domain randomization, sensor simulation, and end-to-end learning, to new user communities. To kickstart education and demonstrate the framework's capabilities, we develop three state-of-the-art policies for small-scale RC cars: controlled drifting, elevation traversal, and visual navigation, each trained in simulation and deployed in the real world. By bridging the gap between advanced Sim2Real methods and affordable, available robotics, Wheeled Lab aims to democratize access to cutting-edge tools, fostering innovation and education in a broader robotics context. The full stack, from hardware to software, is low cost and open-source.