Reinforcement Learning in hyperbolic space for multi-step reasoning
This work addresses multi-step reasoning problems for applications such as mathematical problem-solving and decision-making, representing an incremental advancement by combining existing hyperbolic geometry and Transformer methods in a new RL framework.
The paper tackles multi-step reasoning challenges in AI by integrating hyperbolic Transformers into reinforcement learning, resulting in accuracy improvements of 32-45% and computational time reductions of 16-32% on benchmarks like Frontier Math and nonlinear optimal control.
Multi-step reasoning is a fundamental challenge in artificial intelligence, with applications ranging from mathematical problem-solving to decision-making in dynamic environments. Reinforcement Learning (RL) has shown promise in enabling agents to perform multi-step reasoning by optimizing long-term rewards. However, conventional RL methods struggle with complex reasoning tasks due to issues such as credit assignment, high-dimensional state representations, and stability concerns. Recent advancements in Transformer architectures and hyperbolic geometry have provided novel solutions to these challenges. This paper introduces a new framework that integrates hyperbolic Transformers into RL for multi-step reasoning. The proposed approach leverages hyperbolic embeddings to model hierarchical structures effectively. We present theoretical insights, algorithmic details, and experimental results that include Frontier Math and nonlinear optimal control problems. Compared to RL with vanilla transformer, the hyperbolic RL largely improves accuracy by (32%~44%) on FrontierMath benchmark, (43%~45%) on nonlinear optimal control benchmark, while achieving impressive reduction in computational time by (16%~32%) on FrontierMath benchmark, (16%~17%) on nonlinear optimal control benchmark. Our work demonstrates the potential of hyperbolic Transformers in reinforcement learning, particularly for multi-step reasoning tasks that involve hierarchical structures.