Reinforcement Learning in hyperbolic space for multi-step reasoning

TL;DR

This paper introduces a hyperbolic Transformer-based reinforcement learning framework that significantly improves multi-step reasoning accuracy and efficiency by modeling hierarchical structures more effectively.

Contribution

It presents a novel integration of hyperbolic Transformers into RL, enhancing performance on complex reasoning tasks with theoretical insights and empirical validation.

Findings

Accuracy improved by 32-44% on FrontierMath benchmark

Accuracy improved by 43-45% on nonlinear optimal control benchmark

Computational time reduced by 16-32% on FrontierMath benchmark

Abstract

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.