Hierarchical Reasoning Model

Brain-Inspired Architecture for Deep Reasoning | 27M Parameters | Solves Complex Puzzles with 1000 Examples

Model Statistics

27M Parameters

512 Hidden Size

8 Attention Heads

4+4 H+L Layers

Overview

Forward Pass

Gradient Flow

ACT Mechanism

Architecture Overview

Input Processing

Token Embedding + Puzzle Embedding + Position Encoding

L-Module

Fast, Detailed Computations

4 Transformer Layers
Updates every timestep
Participation Ratio: 30.22

H-Module

Slow, Abstract Strategy

4 Transformer Layers
Updates every L_cycles
Participation Ratio: 89.95

Q-Head for ACT

Halt/Continue Decision

Q(halt) Q(continue)

Forward Pass Flow

Processing Pipeline Details

Each segment processes input through hierarchical modules
L-Module runs 4 times per segment (fast, detailed)
H-Module updates 2 times per segment (slow, strategic)
ACT decides whether to continue or halt after each segment

One-Step Gradient Approximation

Detached States

All intermediate states are detached (no BPTT)

This enables O(1) memory complexity

Memory Comparison

HRM: O(1)

BPTT: O(T)

Adaptive Computation Time

Q-Learning Configuration

State: Hidden representation z_H
Actions: Binary (halt/continue)
Reward: Task accuracy signal
Learning: Online during training

Exploration Strategy

epsilon-greedy with eps = 0.1
Dynamic min_steps sampling
Ensures sufficient computation
Prevents premature halting

Key Features

Hierarchical Convergence:

L-module converges locally, H-module provides global context

Multi-timescale:

Fast L-module (every step) vs Slow H-module (every L_cycles)

No BPTT:

One-step gradient approximation, O(1) memory

ACT:

Adaptive computation via Q-learning

Deep Supervision:

Learning signal at every segment

Performance Highlights

ARC-AGI-1

(beats o3-mini)

40.3%

Sudoku Extreme

accuracy

98.5%

Maze 30x30

optimal paths

99%

Training

examples only!

1000

No pre-training or Chain-of-Thought required!

Brain Correspondence

Dimensionality Hierarchy:

H-module PR=89.95 vs L-module PR=30.22

Similar to Cortex:

Ratio matches mouse cortical hierarchy

Oscillatory Learning:

Inspired by theta-gamma coupling

Local Credit Assignment:

Biologically plausible gradient

Implementation Details

# Core HRM Forward Pass
for segment in range(max_segments):
    # Reset carry for halted sequences
    carry = reset_carry(halted, carry)

    # Hierarchical computation
    for h_step in range(H_cycles):
        for l_step in range(L_cycles):
            z_L = L_level(z_L, z_H + input)
        z_H = H_level(z_H, z_L)

    # ACT decision
    q_halt, q_continue = q_head(z_H)
    if q_halt > q_continue:
        break