Hierarchical Reasoning Model — part 4/4

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Developing a model with the reasoning power of the brain has long been a goal in brain-inspired computing. Spaun 90 is one notable example, which uses spiking neural networks to create distinct modules corresponding to brain regions like the visual cortex and prefrontal cortex. This design enables an architecture to perform a range of cognitive tasks, from memory recall to simple reasoning puzzles. However, its reasoning relies on hand-designed algorithms, which may limit its ability to learn new tasks. Another significant model is the Tolman-Eichenbaum Machine (TEM) 91 , which is inspired by the hippocampal-entorhinal system’s role in spatial and relational memory tasks. TEM proposes that medial entorhinal cells create a basis for structural knowledge, while hippocampal cells link this basis to sensory information. This allows TEM to generalize and explains the emergence of various cell types like grid, border, and place cells. Another approach involves neural sampling models 92 , which view the neural signaling process as inference over a distribution, functioning similarly to a Boltzmann machine. These models often require hand-made rules to be set up for solving a specific reasoning task. In essence, while prior models are restricted to simple reasoning problems, HRM is designed to solve complex tasks that are hard for even advanced LLMs, without pre-training or task-specific manual design.

#### Hierarchical memory

The hierarchical multi-timescale structure also plays an important role in how the brain processes memory. Models such as Hierarchical Sequential Models 93 and Clockwork RNN 94 use multiple recurrent modules that operate at varying time scales to more effectively capture long-range dependencies within sequences, thereby mitigating the forgetting issue in RNNs.

Similar mechanisms have also been adopted in linear attention methods for memorizing long contexts (see the Discussions section). Since HRM focuses on reasoning, full attention is applied for simplicity. Incorporating hierarchical memory into HRM could be a promising future direction.

## 6 Discussions

#### Turing-completeness of HRM

Like earlier neural reasoning algorithms including the Universal Transformer 95 , HRM is computationally universal when given sufficient memory and time constraints. In other words, it falls into the category of models that can simulate any Turing machine, overcoming the computational limitations of standard Transformers discussed previously in the introduction. Given that earlier neural algorithm reasoners were trained as recurrent neural networks, they suffer from premature convergence and memory intensive BPTT. Therefore, in practice, their effective computational depth remains limited, though still deeper than that of a standard Transformer. By resolving these two challenges and being equipped with adaptive computation, HRM could be trained on long reasoning processes, solve complex puzzles requiring intensive depth-first search and backtracking, and move closer to practical Turing-completeness.

#### Reinforcement learning with chain-of-thought

Beyond fine-tuning using human-annotated CoT, reinforcement learning (RL) represents another widely adopted training methodology. However, recent evidence suggests that RL primarily unlocks existing CoT-like capabilities rather than discovering fundamentally new reasoning mechanisms 96 , 97 , 98 , 99 . Additionally, CoT-training with RL is known for its instability and data inefficiency, often requiring extensive exploration and careful reward design. In contrast, HRM takes feedback from dense gradient-based supervision rather than relying on a sparse reward signal. Moreover, HRM operates naturally in a continuous space, which is biologically plausible and avoids allocating same computational resources to each token, even though tokens vary in their reasoning and planning complexity 16 .

#### Linear attention

Recurrence has been explored not only for its capability in universal computation, but also as a means to replace the attention mechanism in Transformers, which suffers from quadratic time and memory complexity 100 . Recurrent alternatives offer a more efficient design by processing input tokens sequentially and predicting the next token at each time step, similar to early RNN-based language models.

Some linear-attention variants, such as Log-linear Attention 101 , share an RNN-like state-update that can be interpreted as propagating multi-timescale summary statistics, thereby retaining long-range context without the quadratic memory growth of standard self-attention. However, substituting the attention mechanism alone does not change the fact that Transformers are still fixed-depth, and require CoT as a compensatory mechanism. Notably, linear attention can operate with a reduced key-value cache over extended contexts, making them more suitable for deployment on resource-constrained edge devices.

## 7 Conclusion

This work introduces the Hierarchical Reasoning Model, a brain-inspired architecture that leverages hierarchical structure and multi-timescale processing to achieve substantial computational depth without sacrificing training stability or efficiency. With only 27M parameters and training on just 1000 examples, HRM effectively solves challenging reasoning problems such as ARC, Sudoku, and complex maze navigation–tasks that typically pose significant difficulties for contemporary LLM and chain-of-thought models.

Although the brain relies heavily on hierarchical structures to enable most cognitive processes, these concepts have largely remained confined to academic literature rather than being translated into practical applications. The prevailing AI approach continues to favor non-hierarchical models. Our results challenge this established paradigm and suggest that the Hierarchical Reasoning Model represents a viable alternative to the currently dominant chain-of-thought reasoning methods, advancing toward a foundational framework capable of Turing-complete universal computation.

Acknowledgements We thank Mingli Yuan, Ahmed Murtadha Hasan Mahyoub and Hengshuai Yao for their insightful discussions and valuable feedback throughout the course of this work.