Paper Group: Hierarchical Reasoning Model

Join us for a paper discussion on "Hierarchical Reasoning Model"
Exploring brain-inspired recurrent architectures for deep computational reasoning without chain-of-thought supervision
Featured Paper:
"Hierarchical Reasoning Model" (Wang et al., 2025)
arXiv Paper | Code
Discussion Topics:
Brain-Inspired Architecture Design

• Two-module recurrent system: high-level (H) for abstract planning, low-level (L) for detailed computation
• Hierarchical convergence prevents premature RNN settling through temporal separation
• Multi-timescale processing mimics cortical theta (4-8Hz) and gamma (30-100Hz) rhythms

Training Innovations

• One-step gradient approximation eliminates BPTT memory requirements (O(1) vs O(T))
• Deep supervision provides intermediate feedback at each reasoning segment
• Adaptive Computation Time (ACT) with Q-learning determines optimal halt points

Performance Benchmarks

| Task Domain | HRM (27M params) | Baseline Methods | Context Size |
| ----------- | ---------------- | ---------------- | ------------ |
| ARC-AGI Challenge | 40.3% | o3-mini: 34.5% | 30×30 grid |
| Sudoku-Extreme | Near-perfect | CoT: 0% | 9×9 grid |
| Maze-Hard (30×30) | Near-perfect | Direct: 0% | 900 tokens |

Implementation Challenges

• Hierarchical convergence timing between H and L modules (T timesteps per cycle)
• Q-learning stability without replay buffers or target networks
• Memory management for multi-segment deep supervision

Key Technical Features

• Trained from scratch with only 1000 examples per task (no pretraining)
• Turing-complete computational depth through recurrent processing
• Participation ratio analysis shows emergent dimensionality hierarchy (H: 89.95, L: 30.22)

Neuroscientific Validation

• High-level module develops higher-dimensional representations than low-level
• Dimensionality hierarchy matches mouse cortex patterns (ratio ≈ 2.98 vs 2.25)
• Emergent property arising during training, not architectural artifact

Future Directions

• Integration with linear attention mechanisms for long-context efficiency
• Extension to multimodal reasoning tasks
• Causal analysis of dimensionality hierarchy necessity

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