This article addresses a fundamental question: How can we enable AI models to perform deep reasoning like the human brain?
In this era of rapid large language model development, we face a critical challenge: current AI systems have significant flaws in their reasoning capabilities. Just as the difference between human infants and adults lies in the depth of thinking, existing AI models, despite their massive parameter scales, are essentially “shallow thinkers.” The Hierarchical Reasoning Model (HRM) aims to solve this core problem.

Rethinking AI Reasoning: From Surface-Level Responses to Deep Thinking

The Fundamental Flaws in Current AI Reasoning

When discussing AI reasoning capabilities, we first need to understand the essence of the problem. Current Transformer architectures, while excelling in natural language processing, face a fundamental limitation: their fixed-depth architecture restricts them to computational complexity classes such as AC0 or TC0, unable to solve problems requiring polynomial time.
What does this mean in practical terms? Even the most advanced GPT models, when facing problems requiring multi-step logical reasoning, remain similar to “fast-food thinkers” capable only of surface-level responses. They lack true “slow thinking” ability—the kind of deep analysis, weighing pros and cons, and step-by-step reasoning that we associate with human intelligence.
Author’s Insight: During my involvement in multiple AI reasoning projects, the most painful aspect wasn’t insufficient model performance, but knowing that the AI was merely skilled at “intelligent-sounding responses” without genuine understanding. This led me to question whether there might be approaches more aligned with human cognitive processes.

The Limitations of Chain-of-Thought Reasoning

Current AI systems primarily rely on Chain-of-Thought (CoT) techniques to simulate reasoning processes. However, this approach has significant problems:

  1. Brittle task decomposition: CoT depends on human-defined decomposition steps, where a small sequencing error can break the entire reasoning chain
  2. Massive training data requirements: CoT needs large amounts of labeled intermediate reasoning steps to learn effectively
  3. Reasoning delays: Each intermediate step requires token generation, causing substantial response time increases

The Human Brain: The Perfect Reasoning Template

Hierarchical Thinking in the Brain

The human brain provides us with the best reference model for reasoning. The brain processes information through hierarchical architectures:

  • High-level areas: Responsible for abstract planning and long-term strategic thinking, operating at slower time scales
  • Low-level areas: Handle concrete details and rapid computations, operating at shorter time scales
    The key feature of this architecture is temporal separation: different brain regions operate at different neural frequencies (such as 4-8Hz theta waves and 30-100Hz gamma waves). This separation ensures stable high-level guidance of low-level computations.

The Power of Feedback Loops

Another characteristic of the brain is the extensive presence of recursive connections. These feedback loops enable the brain to iteratively refine internal representations, gaining more accurate and context-sensitive representations at the cost of increased processing time. This is equivalent to having countless “check and adjust” opportunities during the thinking process.
Practical Application Example: Consider how a lawyer handles complex cases. The HRM works like a lawyer’s thinking process:

  • High-level module: Responsible for overall strategy (prosecution/defense direction, key evidence chain, etc.)
  • Low-level module: Specifically analyzes each piece of evidence, testimony, case law, and other details

HRM Architecture: The Wisdom of Dual-Timescale Collaboration

Core Architectural Principles

HRM’s design is based on three key insights:

  1. Hierarchical processing: Information is processed at different levels of abstraction
  2. Temporal separation: High-level and low-level modules operate at different time scales
  3. Recursive connections: Iterative optimization through feedback loops
    Specifically, HRM contains four learnable components:
  • Input network fI(·;θI)
  • Low-level recurrent module fL(·;θL)
  • High-level recurrent module fH(·;θH)
  • Output network fO(·;θO)

Hierarchical Convergence: Avoiding Premature Convergence

The problem with traditional RNNs is their tendency toward premature convergence—once hidden states approach fixed points, update magnitudes shrink, and subsequent computation becomes ineffective. To solve this problem, HRM introduces the concept of hierarchical convergence:
In each cycle, the low-level module stabilizes to a local equilibrium point, but this equilibrium depends on the high-level state provided during that cycle. After completing T steps, the high-level module uses the converged low-level state and performs its own update, establishing a new context for the low-level module and initiating a new convergence phase.

One-Step Gradient Approximation: Breakthrough in Computational Efficiency

Technical Implementation Example: Traditional BPTT requires O(T) memory to store hidden states for T time steps, causing serious memory bottlenecks in large-scale training. HRM’s one-step gradient approximation method requires only O(1) memory, completely avoiding the need for time unfolding.
The theoretical foundation comes from Deep Equilibrium Models (DEQ), which use the Implicit Function Theorem (IFT) to bypass BPTT. When recurrent neural networks converge to fixed points, we can apply backpropagation at that equilibrium point, avoiding state sequence unfolding.
Implementation Details:

def hrm(z, x, N=2, T=2):
    x = input_embedding(x)
    zH, zL = z
    
    with torch.no_grad():
        for _i in range(N * T - 1):
            zL = L_net(zL, zH, x)
            if (_i + 1) % T == 0:
                zH = H_net(zH, zL)
    
    # One-step gradient
    zL = L_net(zL, zH, x)
    zH = H_net(zH, zL)
    
    return (zH, zL), output_head(zH)

Adaptive Computation Time: Teaching AI to Think Fast and Slow

The Innovative Mechanism of Deep Supervision

Practical Application Scenario: In medical diagnosis scenarios, facing minor symptoms versus critical conditions, the model needs to learn to allocate different “thinking times.” The deep supervision mechanism enables HRM to:

  1. Perform multiple forward passes for each training sample, each called a segment
  2. After each segment, use “detach” operations to disconnect hidden states from the computation graph
  3. Gradients from segment m+1 don’t backpropagate through segment m, creating a one-step approximation of the recursive deep supervision process

Q-Learning Driven Adaptive Stopping

Specific Application Case: In software development, like programmers debugging complex bugs. HRM’s Adaptive Computation Time (ACT) mechanism mirrors this process:

  • “Halt” action: When sufficiently satisfied with the solution, stop debugging
  • “Continue” action: When deeper debugging and analysis is needed, continue thinking
    ACT uses Q-learning algorithms to adaptively determine segment numbers. A Q-head uses the final state of the H-module to predict Q-values for “halt” and “continue” actions:
Qm = σ(θQ^T zmNT_H)

Where σ is the element-wise applied sigmoid function. The halt or continue action selection uses a stochastic strategy, defining maximum Mmax and minimum Mmin threshold mechanisms.
Practical Runtime Effect: On Sudoku-Extreme-Full, ACT models maintain low and stable average computation steps even as the Mmax parameter increases. Meanwhile, ACT models achieve performance comparable to fixed-computation models while utilizing substantially fewer computation steps on average.

Experimental Results: Revolutionary Breakthrough in Data Efficiency

Benchmark Performance

HRM demonstrates remarkable performance across three key benchmarks:
ARC-AGI Challenge:

  • ARC-AGI-1: 40.3% accuracy, surpassing o3-mini-high (34.5%) and Claude 3.7 8K (21.2%)
  • ARC-AGI-2: 74.5% accuracy, significantly outperforming other models
    Sudoku-Extreme:
  • Near-perfect performance (>95% accuracy) with 1000 training samples
  • Traditional CoT methods fail almost completely under the same conditions
    30×30 Maze Navigation:
  • 74.5% accuracy with 1000 training samples
  • Far superior performance compared to other large models

Parameter Scale Comparison

Particularly noteworthy is that HRM achieves this performance with only 27 million parameters, significantly lower than many baseline models. This means it maintains high performance while having better computational efficiency and lower deployment costs.
Author’s Insight: This result reminds me of a profound observation—not all “big” is good. In AI, we often habitually assume larger models will perform better, but HRM proves that elegant architectural design can surpass simple parameter stacking.

Brain Correspondence: Striking Similarities to Biological Intelligence

Discovery of Participation Ratio (PR) in Biology

In systems neuroscience, a fundamental principle is that a brain region’s functional repertoire is closely linked to its neural representation dimensionality. High-level cortical areas responsible for complex reasoning and decision-making need to handle various tasks, requiring more flexible and context-dependent processing.
Experimental Discovery: HRM perfectly reproduces this principle. After training on Sudoku tasks:

  • Low-level module state (zL) occupies a relatively small subspace with participation ratio of 30.22
  • High-level module state (zH) operates in a substantially larger subspace with participation ratio of 89.95
    More importantly, HRM’s high-level module dimensionality scales correspondingly with the number of tasks (expanding from PR values for 10 tasks to 100 tasks), while low-level module dimensionality remains stable. This indicates emergent separation of representational capacity between modules, paralleling their functional roles.
    Biological Comparison: This high-to-low PR ratio (~2.98) in HRM closely matches measurements in mouse cortex (~2.25)! This strongly suggests HRM has discovered a fundamental organizational principle.

Deep Visualization: Observing AI’s Thinking Process

Analysis of Intermediate Time Steps

Through state trajectory analysis, we can directly observe how HRM handles different problem types:
Maze Task Analysis:
HRM appears to initially explore several potential paths simultaneously, subsequently eliminating blocked or inefficient routes, then constructing preliminary solution outlines followed by multiple optimization iterations. This resembles human strategy in complex path planning: quickly evaluate several possible solutions, then progressively refine them.
Sudoku Task Analysis:
The strategy is more akin to depth-first search, where the model seems to explore potential solutions and backtracks when encountering dead ends. This indeed matches human thinking patterns when solving Sudoku—trying a digit placement first, then backtracking to previous decision points when conflicts are discovered.
ARC Task Analysis:
Unlike Sudoku’s frequent backtracking, ARC solution paths follow more consistent progression, similar to hill-climbing optimization. The model gradually adjusts grid content until reaching solutions.
Practical Application Insights: These visualization results tell us that HRM not only outperforms traditional methods in performance, but more importantly, it learns to adopt different effective strategies for different problem types. This is exactly what we expect from intelligent systems—adaptability.

Practical Applications: Success Stories in the Real World

Programming Problem Solving

Imagine a scenario where HRM assists programmers in solving complex algorithmic problems. Traditional methods might require specialized solutions for each specific problem, while HRM can:

  1. Analyze problem structure: Automatically identify problem types (sorting, graph search, dynamic programming, etc.)
  2. Decompose solution strategies: Break complex problems into manageable sub-problems
  3. Generate solutions: Not simple code copying, but genuine understanding-based solutions
    Application Prospects: In scenarios like code review, bug fixing, and performance optimization, HRM has enormous application potential.

Scientific Discovery Assistance

In scientific research, HRM can help scientists handle hypothesis generation and validation requiring complex reasoning:
Drug Discovery:

  • High-level module: Analyzes disease molecular mechanisms, develops research strategies
  • Low-level module: Calculates molecular interactions, evaluates candidate compounds
    Materials Science:
  • High-level module: Proposes material design directions based on theoretical physics principles
  • Low-level module: Simulates material properties, optimizes molecular structures

Decision Support Systems

In business and policy-making, HRM’s multi-level thinking pattern is particularly valuable:
Risk Assessment:

  • High-level module: Analyzes overall risk landscape, develops risk mitigation strategies
  • Low-level module: Calculates specific risk event probabilities and impacts
    Resource Allocation:
  • High-level module: Develops resource allocation strategies based on organizational goals and constraints
  • Low-level module: Optimizes specific resource allocation decisions

Technical Advantages Analysis

Breakthrough in Computational Efficiency

Unlike traditional Transformers requiring massive pre-training and CoT data, HRM’s core advantages include:

  1. Sample efficiency: Achieves near-optimal performance with only 1000 samples
  2. Memory efficiency: O(1) memory requirement vs BPTT’s O(T) provides substantial savings
  3. Training stability: Avoids traditional deep network gradient vanishing problems

Architectural Scalability

Inference-time computational scaling:
HRM’s another significant advantage is inference-time computational scaling. Simply increasing the Mmax parameter, without further training or architectural modifications, allows the model to utilize additional computational resources during inference.
Practical Testing: Models trained with Mmax=8 on Sudoku tasks continue to see accuracy improvements when run with Mmax=16 during inference. This indicates the model has learned to utilize computational resources effectively, which is very useful for performance tuning in practical applications.

Future Development Directions

Integration with Reinforcement Learning

Current reinforcement learning training primarily unlocks existing CoT capabilities rather than discovering entirely new reasoning mechanisms. HRM’s continuous space operation provides new possibilities for more natural RL integration.

Linear Attention Mechanisms

HRM’s multi-timescale processing also inspires attention mechanism optimization directions. Combining hierarchical structures with linear attention might be a new approach to solving long context processing challenges.

Neuromorphic Computing

HRM’s design naturally aligns with neuromorphic computing, giving it unique advantages in hardware implementation, especially for edge devices requiring low power consumption and high parallelism.

Industry Impact and Insights

Redefining AI Reasoning Standards

HRM’s proposal marks a paradigm shift in AI reasoning capabilities. From relying on surface-level responses (CoT) to genuine deep thinking, this change may redefine what constitutes “intelligent” AI systems.
Insights for Enterprises:

  • Technical decisions: May need to reassess dependence on large language models
  • R&D investment: Focus might shift from model scaling growth to architectural innovation investment
  • Application development: More attention to reasoning quality rather than surface conversational ability

Rethinking Talent Development

As technologies like HRM develop, AI practitioners need:

  • Deep understanding of cognitive science and neuroscience principles
  • Cross-domain knowledge integration capabilities
  • Systematic thinking and problem decomposition abilities
    Author’s Reflection: As a technical expert, I deeply feel the importance of continuous learning. We cannot merely satisfy ourselves with mastering current technology stacks, but should actively understand the latest discoveries in foundational disciplines like cognitive science and neuroscience. This cross-disciplinary knowledge integration will be key to future AI development.

Challenges and Limitations

Technical Challenges

While HRM shows enormous potential, it still faces some challenges:

  1. Training stability: Despite avoiding some traditional problems, stable training of deep architectures still requires fine-tuning
  2. Computational complexity: While memory efficiency is improved, time complexity remains relatively high
  3. Interpretability: The interpretability of internal representations requires further research

Application Limitations

  1. Domain adaptability: Model robustness when transferring between different domains needs validation
  2. Computational resource requirements: High computational demands during inference might limit real-time applications
  3. Data dependency: Requirements for training data quality and quantity remain relatively high

Conclusion and Outlook

Summary of Key Contributions

HRM represents an important breakthrough in AI reasoning capabilities:

  1. Architectural innovation: Introduces hierarchical multi-timescale computational architecture
  2. Efficiency improvement: Improves performance while significantly reducing parameters and training samples
  3. Theoretical contribution: Provides new perspective on relationship between computational depth and actual performance
  4. Biological significance: Demonstrates striking similarities to biological brain organization

Profound Impact on AI Development

HRM’s success reminds us that true artificial general intelligence may not come from simple model scaling, but from deep understanding and precise simulation of cognitive processes. This biologically inspired design approach points the way for future AI research.
Future Vision: We are witnessing a shift in AI from “eloquent speech” to “deep thinking.” This transformation will redefine the capability boundaries of intelligent systems, paving the way for solving more complex problems.

Frequently Asked Questions (FAQ)

Q1: What are the fundamental differences between HRM and traditional Transformers?
A: Traditional Transformers use fixed-depth feedforward architectures, while HRM employs hierarchical recurrent structures achieving true deep reasoning through multi-timescale layers.
Q2: Why can HRM achieve high performance with only 1000 training samples?
A: The hierarchical architecture allows HRM to utilize limited training data more effectively, while the one-step gradient approximation method avoids complex BPTT training, focusing on core reasoning capability learning.
Q3: How does ACT adaptive computation time work?
A: ACT uses Q-learning algorithms, enabling the model to decide “thinking time” based on problem complexity—quick resolution for simple problems, deep thinking for complex ones.
Q4: Can HRM’s reasoning process be visualized?
A: Yes. Through intermediate state trajectory analysis, we can observe how the model gradually builds solutions, explores paths, and optimizes decisions, similar to human thinking processes.
Q5: What future application domains might HRM have?
A: Programming assistance, scientific discovery, decision support systems, medical diagnosis, risk assessment, and other scenarios requiring complex reasoning.
Q6: Does HRM mean the end of CoT technology?
A: Not exactly. HRM’s latent reasoning concept may be a powerful complement to CoT, especially in scenarios requiring precise reasoning without generating lengthy explanations.
Q7: How to evaluate HRM’s learning effectiveness?
A: Through participation ratio (PR) analysis, state trajectory visualization, intermediate prediction monitoring, and other methods to observe model learning processes and reasoning strategies.
Q8: How does HRM’s computational efficiency compare to other methods?
A: HRM uses O(1) memory (vs BPTT’s O(T)), achieving high performance while substantially reducing computational resource requirements, particularly suitable for resource-constrained deployment environments.

Practical Summary and Action Checklist

Implementation Checklist

  • [ ] Understand core concepts of hierarchical architecture
  • [ ] Choose appropriate hierarchical separation strategies
  • [ ] Implement one-step gradient approximation method
  • [ ] Configure adaptive computation time mechanisms
  • [ ] Design appropriate supervision strategies
  • [ ] Verify model performance on target tasks

Performance Optimization Suggestions

  • Prioritize stable deep supervision mechanisms
  • Carefully tune ACT hyperparameters
  • Ensure sufficient capacity differentiation between different levels
  • Monitor convergence behavior during training

Deployment Considerations

  • Consider inference-time computational scaling requirements
  • Reserve sufficient computational resources for complex problems
  • Establish appropriate application scenario filtering mechanisms
  • Implement progressive deployment strategies to reduce risks