Hierarchical Reasoning Model

Paper: https://www.alphaxiv.org/abs/2506.21734

Context

Abstract Reasoning Corpus (ARC)

This paper aims at solving ARC using minimal amount of computation with a new archtecture.

Thinking Fast, Thking Slow:

  • Lots of research papers refer to this book
  • The book talks divides brain’s thinking process into slow and fast
    • Fast: Fast, Automatic, Intuitive
    • Slow: Deloberate, effortful reasoning
Hierarchical Reasoning process

Introduction

Previous reasoning models use CoT (Chain-of-Thought), downsides:

  • Brittle task decomposition: Single misstep can break the chain
  • Extensive data requirements: Large training data
  • High latency: Generates loads of token; slowing down inference

WHat are they offering: Latenet Reasoning

  • Language is for human communication and ideas/thoughts are compressed effectively without translating back to language
  • The model operates within its own hidden state

Inspired by human brain

  • High-level (slow) part and low-level (fast) part interact
  • The low-level exectures ideas based on the global knowdlege stored in High-level
  • High-level gets feedback from low-level and adjusts
  • Hierarchy and multi-stage

Datasets

Hierarchical Reasoning process

Result

  • Models being compared are general purpose
  • Not tested on ARC-3
Comparison for ARC-1,2, and Soduku (Figure 1 from paper)

Method

Data + Augmentations

1000 From each (ARC, Sudoku, Maze) + ==≥ 3,831,994

  • ARC: transition/rotations/flips/color permutations
  • Soduku: used band and digits permuations
  • Maze: No change, raw data used

H-L combo

  • H-level updates after T steps of L-level
    • When L-level reeaches local equilibrium
  • H-level’s world-view changes; L-level resets -≥ new computation path
  • N (number of H update) x L (number of l updates) increase the reasoning depth
Hierarchical Reasoning process

Memory footprint

Backpropagation Through Time (BPTT) saves model parameters at each time step and backpropagates.

  • Biological implausibility: Human brain does not do this

This approach is O(1): Constant memory; uses one-step gradient approximation::uses the first and last state of H and L level, intermediary steps as constants.

  • Aligns with idea of local rule in brian
  • Brain does not utilize all previous computations for learning

More Detailed Result

ARC-AGI Performance Comparison (HRM vs. Baselines)

Model Size (Params) ARC-AGI-1 (%) ARC-AGI-2 (%) Pretraining? CoT Used? Notes
No Pretraining + No CoT (Trained from scratch, minimal supervision)            
HRM ~27M 40.3 5.0 ❌ ❌ Proposed model; uses hierarchical recurrence, latent reasoning
Direct pred (8-layer Transformer) ~27M 15.8 ~0.0 (implied) ❌ ❌ Same size as HRM, but standard architecture fails on hard tasks
Liao & Gu (equivariant CNN) ~10–50M (est.) 15.8 Not reported ❌ ❌ Specialized architecture tailored to ARC; hand-designed inductive biases
             
Pretrained + CoT-Based (Large language models using step-by-step prompting)            
o3-mini-high (GPT-4o variant) ~48B 34.5 1.3 ✅ ✅ Top CoT model in evaluation; uses 128k context
Claude 3.7 8K ~100–200B (est.) 21.2 0.9 ✅ ✅ Proprietary model; strong CoT capability
Deepseek R1 (est.) ~100B+ ~21.0 ~0.0 ✅ ✅ Estimated performance based on plot in paper
             
Pretrained + CoT (Other Notable Models)            
AlphaGeometry 2 ~100B+ ~20–25 (est.) Not tested ✅ ✅ Specialized for geometric puzzles, not full ARC-AGI
GPT-4o (Base) ~48B ~30–35 (varies) N/A ✅ ✅ Public results vary; performance depends on prompt engineering

🔍 Key Insights:

  • HRM is in a different league: Despite using no pretraining, no CoT, and 1,000× fewer parameters, it outperforms all CoT-based models on ARC-AGI-1.
  • Efficiency: HRM achieves 40.3% on ARC-AGI-1 using only 960 training examples and 27M parameters — a level of data and parameter efficiency unmatched by any other model.
  • CoT limitations: Even the strongest CoT models struggle with ARC-AGI-2, which requires compositional, multi-step abstraction — suggesting CoT has fundamental limits on novel reasoning.
  • Architecture > Scale: HRM proves that better internal reasoning design can beat scaling alone — a shift from “bigger is better” to “deeper, structured computation wins.”

This hierarchical view underscores HRM’s significance: it achieves superior reasoning not by being larger or more data-hungry, but by thinking differently — deeply, internally, and adaptively.

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