Hierarchical Reasoning Model

Abstract: Reasoning, the process of devising and executing complex goal-oriented action sequences, remains a critical challenge in AI. Current LLMs primarily employ Chain-of-Thought (CoT) techniques, which suffer from brittle task decomposition, extensive data requirements, and high latency. Inspired by the hierarchical and multi-timescale processing in the human brain, we propose the Hierarchical Reasoning Model (HRM), a novel recurrent architecture that attains significant computational depth while maintaining both training stability and efficiency. HRM executes sequential reasoning tasks in a single forward pass without explicit supervision of the intermediate process, through two interdependent recurrent modules: a high-level module responsible for slow, abstract planning, and a low-level module handling rapid, detailed computations. With only 27 million parameters, HRM achieves exceptional performance on complex reasoning tasks using only 1000 training samples. The model operates without pre-training or CoT data, yet achieves nearly perfect performance on challenging tasks including complex Sudoku puzzles and optimal path finding in large mazes. Furthermore, HRM outperforms much larger models with significantly longer context windows on the Abstraction and Reasoning Corpus (ARC), a key benchmark for measuring artificial general intelligence capabilities. These results underscore HRM's potential as a transformative advancement toward universal computation and general-purpose reasoning systems.

• The paper introduces a novel hierarchical model that overcomes limitations of CoT techniques by leveraging multi-timescale processing.
• The model employs a brain-inspired architecture with coupled recurrent modules, adaptive computation time, and deep supervision for efficient training.
• Experimental results on ARC, Sudoku, and Maze benchmarks demonstrate near-perfect performance with only 27M parameters and limited training data.

Hierarchical Reasoning Model: A Novel Architecture for Enhanced Computational Depth

The paper "Hierarchical Reasoning Model" (2506.21734) introduces a novel recurrent neural network architecture, the Hierarchical Reasoning Model (HRM), inspired by the hierarchical and multi-timescale processing observed in the human brain. The HRM aims to address the limitations of current LLMs in complex reasoning tasks by achieving significant computational depth while maintaining training stability and efficiency. The model demonstrates exceptional performance on challenging reasoning tasks, achieving near-perfect accuracy on complex Sudoku puzzles and optimal path finding in large mazes with limited training data and without relying on Chain-of-Thought (CoT) techniques.

Architectural Design and Principles

The HRM architecture is based on three key principles derived from neural computation in the brain: hierarchical processing, temporal separation, and recurrent connectivity. It comprises two coupled recurrent modules: a high-level (H) module responsible for abstract planning and a low-level (L) module for detailed computations. This hierarchical structure facilitates a process termed "hierarchical convergence," where the H-module updates at a slower timescale, guiding the L-module's computations and preventing premature convergence. The H-module advances only after the L-module has completed multiple computational steps and reached a local equilibrium, at which point the L-module is reset to begin a new computational phase.

Figure 1: HRM is inspired by hierarchical processing and temporal separation in the brain. It has two recurrent networks operating at different timescales to collaboratively solve tasks. With only about 1000 training examples, the HRM (\textasciitilde27M parameters) surpasses state-of-the-art CoT models on inductive benchmarks (ARC-AGI) and challenging symbolic tree-search puzzles (Sudoku-Extreme, Maze-Hard) where CoT models failed completely. The HRM was randomly initialized, and it solved the tasks directly from inputs without chain of thoughts.

Formally, the HRM model consists of four learnable components: an input network $f_I(\cdot; \theta_I)$, a low-level recurrent module $f_L(\cdot; \theta_L)$, a high-level recurrent module $f_H(\cdot; \theta_H)$, and an output network $f_O(\cdot; \theta_O)$. The model's dynamics unfold over $N$ high-level cycles of $T$ low-level timesteps each. At each timestep $i$, the L-module updates its state conditioned on its own previous state, the H-module’s current state (which remains fixed throughout the cycle), and the input representation.

Training Methodology: Approximate Gradient and Deep Supervision

The HRM employs a one-step gradient approximation for training, which offers improved efficiency and eliminates the need for Backpropagation Through Time (BPTT). This approach maintains a constant memory footprint ($O(1)$) throughout backpropagation, making it scalable and biologically plausible. The gradient path is as follows: Output head $\rightarrow$ final state of the H-module $\rightarrow$ final state of the L-module $\rightarrow$ input embedding. This method leverages the Implicit Function Theorem (IFT) from Deep Equilibrium Models (DEQ) to approximate the gradient without unrolling the recurrent network.

Inspired by periodic neural oscillations that regulate learning in the brain, the HRM incorporates a deep supervision mechanism. Multiple forward passes of the HRM model are executed, and at each segment $m$, a deep supervision step is applied. The hidden state $z^m$ is detached from the computation graph before being used as the input state for the next segment, effectively creating a 1-step approximation of the gradient. This provides more frequent feedback to the H-module and serves as a regularization mechanism.

Adaptive Computation Time

The HRM incorporates an adaptive halting strategy inspired by the brain's dynamic alternation between automatic and deliberate reasoning. This mechanism, termed Adaptive Computation Time (ACT), leverages deep supervision and uses the Q-learning algorithm to adaptively determine the number of segments. A Q-head predicts the Q-values for "halt" and "continue" actions based on the final state of the H-module. The halt or continue action is chosen using a randomized strategy, allowing the model to dynamically modulate its "runtime" based on task complexity and potential rewards. The overall loss for each supervision segment combines both the Q-head loss and the sequence-to-sequence loss: $$L^m_\text{ACT} = Loss(\hat{y}^m, y) + BinaryCrossEntropy(\hat{Q}^m, \hat{G}^m)$$. This enables both accurate predictions and nearly optimal stopping decisions.

Figure 2: Effectiveness of Adaptive Computation Time (ACT) on the Sudoku-Extreme-Full. (a) Mean compute steps used by models with ACT versus models with a fixed number of compute steps (M). ACT maintains a low and stable number of average compute steps even as the maximum limit ($M_{\max}$) increases.

Experimental Results and Benchmarks

The HRM was evaluated on several challenging reasoning benchmarks, including ARC-AGI, Sudoku-Extreme, and Maze-Hard. These benchmarks were selected to evaluate various reasoning abilities in AI models. The results demonstrate that HRM achieves state-of-the-art performance on these tasks with limited training data and without pre-training or CoT labels.

On the Abstraction and Reasoning Corpus (ARC) AGI Challenge, HRM, trained from scratch with only the official dataset (\textasciitilde1000 examples), with only 27M parameters and a 30x30 grid context (900 tokens), achieves a performance of 40.3\%, which substantially surpasses leading CoT-based models. For example, it achieves near-perfect accuracy in complex Sudoku puzzles (Sudoku-Extreme Full) and optimal pathfinding in 30x30 mazes, where state-of-the-art CoT methods completely fail (0\% accuracy).

Figure 3: The necessity of depth for complex reasoning. Left: On Sudoku-Extreme Full, which require extensive tree-search and backtracking, increasing a Transformer's width yields no performance gain, while increasing depth is critical. Right: Standard architectures saturates, failing to benefit from increased depth. HRM overcomes this fundamental limitation, effectively using its computational depth to achieve near-perfect accuracy.

Brain Correspondence: Hierarchical Dimensionality Organization

The paper explores the correspondence between the HRM and the brain by analyzing the dimensionality of neural representations in the model's recurrent modules. Higher-order cortical areas, responsible for complex reasoning and decision-making, exhibit higher-dimensional state-space trajectories. The Participation Ratio (PR) is used as a measure of the effective dimensionality of high-dimensional representations. The results show that the H-module in HRM operates in a substantially larger subspace compared to the L-module, mirroring the dimensionality hierarchy observed in the mouse cortex. This suggests that the model has discovered a fundamental organizational principle that is essential for robust and flexible reasoning in biological systems.

Figure 4: Hierarchical Dimensionality Organization in the HRM and Mouse Cortex. (a,b) are adapted from~\citet{posani2025rarely}.

Conclusion

The HRM represents a significant advancement in the development of AI reasoning systems. By leveraging a brain-inspired architecture with hierarchical structure, multi-timescale processing, and adaptive computation, the HRM achieves exceptional performance on challenging reasoning tasks with limited training data. The model's ability to solve complex problems without relying on CoT techniques and its correspondence to neuroscientific principles suggest that it has the potential to serve as a foundational framework for Turing-complete universal computation.