Hierarchical Reasoning Model

arxiv:2506.21734

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Reasoning and the "physics" of language models · 2025-06-26

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1. Part 1
2. Part 2
3. Part 3
4. Part 4

Contents

• Hierarchical Reasoning Model
• Abstract
• 1 Introduction
• 2 Hierarchical Reasoning Model
• Hierarchical convergence
• Approximate gradient
• Deep supervision
• Adaptive computational time (ACT)
• Inference-time scaling
• Stability of Q-learning in ACT
• Architectural details
• 3 Results
• 3.1 Benchmarks
• 3.2 Evaluation Details
• 3.3 Visualization of intermediate timesteps
• 4 Brain Correspondence
• 5 Related Work
• Reasoning and algorithm learning
• Brain-inspired reasoning architectures
• Hierarchical memory
• 6 Discussions
• Turing-completeness of HRM
• Reinforcement learning with chain-of-thought
• Linear attention
• 7 Conclusion