Hierarchical Reasoning Model (HRM) is a novel approach using two small neural networks recursing at different frequencies.
This biologically inspired method beats Large Language models (LLMs) on hard puzzle tasks such as Sudoku, Maze, and ARC-AGI while trained with small models (27M parameters) on small data (around 1000 examples). HRM holds great promise for solving hard problems with small networks, but it is not yet well understood and may be suboptimal.
We propose Tiny Recursive Model (TRM), a much simpler recursive reasoning approach that achieves significantly higher generalization than HRM, while using a single tiny network with only 2 layers.
With only 7M parameters, TRM obtains 45% test-accuracy on ARC-AGI-1 and 8% on ARC-AGI-2, higher than most LLMs (e.g., Deepseek R1, o3-mini, Gemini 2.5 Pro) with less than 0.01% of the parameters.
" With only 7M parameters,
TRM obtains 45% test-accuracy on ARC-AGI-
1 and 8% on ARC-AGI-2, higher than most
LLMs (e.g., Deepseek R1, o3-mini, Gemini 2.5
Pro) with less than 0.01% of the parameters"
That is very impressive.
Side note:
Superficially reminds me of Hierarchical Temporal Memory from Jeff Hawkins "On Intelligence".
Although this doesn't have the sparsity aspect, its hierarchical and temporal aspects are related.
So what happens when we figure out how to 10x both scale and throughput on existing hardware by using it more efficiently? Will gigantic models still be useful?
Wow, so not only are the findings from https://arxiv.org/abs/2506.21734 (posted on HN a while back) confirmed, they're generalizable? Intriguing. I wonder if this will pan out in practical use cases, it'd be transformative.
Also would possibly instantly void the value of trillions of pending AI datacenter capex, which would be funny. (Though possibly not for very long.)
With the same data augmentation / 'test time training' setting, the vanilla Transformers do pretty well, close to the "breakthrough" HRM reported. From a brief skim, this paper is using similar settings to compare itself on ARC-AGI.
I too, want to believe in smaller models with excellent reasoning performance. But first understand what ARC-AGI tests for, what the general setting is -- the one that commercial LLMs use to compare against each other -- and what the specialised setting HRM and this paper uses as evaluation.
The naming of that benchmark lends itself to hype, as we've seen in both HRM and this paper.
The TRM paper addresses this blog post. I don't think you need to read the HRM analysis very carefully, the TRM has the advantage of being disentangled compared to the HRM, making ablations easier. I think the real value of the arcprize HRM blog post is to highlight the importance of ablation testing.
I think ARC-AGI was supposed to be a challenge for any model. The assumption being that you'd need the reasoning abilities of large language models to solve it. It turns out that this assumption is somewhat wrong. Do you mean that HRM and TRM are specifically trained on a small dataset of ARC-AGI samples, while LLMs are not? Or which difference exactly do hint at?
I implemented HRM for educational purposes and got good results for path finding. But then I started to do ablation experiments and came to the same conclusions as the ARC-AGI team (the HRM architecture itself didn’t play a big role): https://github.com/krychu/hrm
This was a bit unfortunate. I think there is something in the idea of latent space reasoning.
Overall I really like these transformer RNNs. They are basically EBMs learning an energy landscape that falls into a solution, relaxing a discrete problem into a smooth convex one. Reminds me of other iterative methods like neural cellular automata and flow matching / diffusion. This method looks promising for control problems: just tumble your way down the state space, where each step is constrained to be a valid action.
Makes me think once again about the similarity to Finite Impulse Response[1] filters (traditional LLMs) and Infinite Impulse Response[2] filters (recursive models). Not that it's a very good or original analogy.
Anyway, with FIR you typically need many, many times the coefficients to get similar filter cutoff performance as a what few IIR coefficients can do.
You can convert a IIR to a FIR using for example the window design method[3], where if you use a rectangular window function you essentially unroll the recursion but stop after some finite depth.
Similarly it seems unrolling the TRM you end up with the traditional LLM architecture of many repeated attention+ff blocks, minus the global feedback part. And unlike a true IIR, the TRM does implement a finite cut-off, so in that sense is more like a traditional FIR/LLM than the structure suggest.
So, would perhaps be interesting to compare the TRM network to a similarly unrolled version.
Then again, maybe this is all mad ramblings from a sleep deprived mind.
Any idea why the tiny network takes days to run on massive GPUs? is it the large dataset, or the recursive nature of the algorithm? i.e. would a simple question take hours to solve or require a huge amount of memory?
I don't have a huge amount of experience in the nitty gritty details and I'm wondering if I'll be able to run some interesting training on a 3090 in a few days.
Very cool to see the effectiveness of recurrence on ARC. For those interested in recurrence, here are other works that leverage a similar approach for other types of problems:
Oh boy. Is this not essentially a neuralese CoT? They’re explicitly labelling z/z_L as a reasoning embedding that persists/mutates through the recursive process, used to refine the output embedding z_H/y. Is this not literally a neuralese CoT/reasoning chain? Yikes!
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[ 2.2 ms ] story [ 50.1 ms ] threadHierarchical Reasoning Model (HRM) is a novel approach using two small neural networks recursing at different frequencies.
This biologically inspired method beats Large Language models (LLMs) on hard puzzle tasks such as Sudoku, Maze, and ARC-AGI while trained with small models (27M parameters) on small data (around 1000 examples). HRM holds great promise for solving hard problems with small networks, but it is not yet well understood and may be suboptimal.
We propose Tiny Recursive Model (TRM), a much simpler recursive reasoning approach that achieves significantly higher generalization than HRM, while using a single tiny network with only 2 layers.
With only 7M parameters, TRM obtains 45% test-accuracy on ARC-AGI-1 and 8% on ARC-AGI-2, higher than most LLMs (e.g., Deepseek R1, o3-mini, Gemini 2.5 Pro) with less than 0.01% of the parameters.
That is very impressive.
Side note: Superficially reminds me of Hierarchical Temporal Memory from Jeff Hawkins "On Intelligence". Although this doesn't have the sparsity aspect, its hierarchical and temporal aspects are related.
https://en.wikipedia.org/wiki/Hierarchical_temporal_memory https://www.numenta.com
Also would possibly instantly void the value of trillions of pending AI datacenter capex, which would be funny. (Though possibly not for very long.)
With the same data augmentation / 'test time training' setting, the vanilla Transformers do pretty well, close to the "breakthrough" HRM reported. From a brief skim, this paper is using similar settings to compare itself on ARC-AGI.
I too, want to believe in smaller models with excellent reasoning performance. But first understand what ARC-AGI tests for, what the general setting is -- the one that commercial LLMs use to compare against each other -- and what the specialised setting HRM and this paper uses as evaluation.
The naming of that benchmark lends itself to hype, as we've seen in both HRM and this paper.
I think ARC-AGI was supposed to be a challenge for any model. The assumption being that you'd need the reasoning abilities of large language models to solve it. It turns out that this assumption is somewhat wrong. Do you mean that HRM and TRM are specifically trained on a small dataset of ARC-AGI samples, while LLMs are not? Or which difference exactly do hint at?
This was a bit unfortunate. I think there is something in the idea of latent space reasoning.
Anyway, with FIR you typically need many, many times the coefficients to get similar filter cutoff performance as a what few IIR coefficients can do.
You can convert a IIR to a FIR using for example the window design method[3], where if you use a rectangular window function you essentially unroll the recursion but stop after some finite depth.
Similarly it seems unrolling the TRM you end up with the traditional LLM architecture of many repeated attention+ff blocks, minus the global feedback part. And unlike a true IIR, the TRM does implement a finite cut-off, so in that sense is more like a traditional FIR/LLM than the structure suggest.
So, would perhaps be interesting to compare the TRM network to a similarly unrolled version.
Then again, maybe this is all mad ramblings from a sleep deprived mind.
[1]: https://en.wikipedia.org/wiki/Finite_impulse_response
[2]: https://en.wikipedia.org/wiki/Infinite_impulse_response
[3]: https://en.wikipedia.org/wiki/Finite_impulse_response#Window...
I don't have a huge amount of experience in the nitty gritty details and I'm wondering if I'll be able to run some interesting training on a 3090 in a few days.
Language modeling:
Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach https://arxiv.org/pdf/2502.05171
Puzzle solving:
A Simple Loss Function for Convergent Algorithm Synthesis using RNNs https://openreview.net/pdf?id=WaAJ883AqiY
End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking https://arxiv.org/abs/2202.05826
Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks https://proceedings.neurips.cc/paper/2021/file/3501672ebc68a...
General:
Think Again Networks and the Delta Loss https://arxiv.org/pdf/1904.11816
Universal Transformers https://arxiv.org/abs/1807.03819
Adaptive Computation Time for Recurrent Neural Networks https://arxiv.org/pdf/1603.08983