SearcharxivSearch

arXiv · 2609.22197

Dissecting Hierarchical Reasoning Models: A Mechanistic Study

Abstract

We study Hierarchical Reasoning Model (HRM), a representative hierarchical Transformer-based latent reasoning model with many variants, on Sudoku, Maze, and ARC-AGI-2. We mechanistically understand how HRM reasons and what information it encodes. Our analyses compare HRM against Transformer baselines with and without recurrent modules, apply causal interventions on recurrent states, and utilize linear probes against random-direction ablations, as well as sparse autoencoders with feature ablations. Our results reveal several key findings: recurrent models outperform one-pass baselines, while single-state recurrent Transformers are comparable to HRM. State interventions further show that the causal contributions of the high- and low-level states vary across task-specific checkpoints and inference stages. Selected task variables are linearly decodable from the recurrent states in HRM, yet ablating probe directions produce effects comparable to random controls. SAE ablations yield larger behavioral changes than probe-direction ablations. However, top-ranked SAE features show no stable advantage over size-matched random subsets at larger ablation sizes or across tasks; the same pattern persists in a Sudoku control with within-step BPTT. Together, we characterize that HRM is essentially implementing constraint-aware iterative refinement on a puzzle-specific solution state, in which the functional contributions of components at different levels vary without relying on a compact, causally important feature set. These results highlight the necessity of studying the different working mechanisms and the importance of developing mechanistic interpretability techniques better suited for latent-space, recursive reasoning models.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Leo Raphael Rodrigues, Jian Kang. 2026-08-30. Dissecting Hierarchical Reasoning Models: A Mechanistic Study. https://arxiv.org/abs/2609.22197

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data

We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of a random Tikhonov regularization path and decompose the tracking error of the algorithm's output for the regularization path into random difference equations in RKHS. We show that the tracking error vanishes in mean square and almost surely if the regularization path is slowly time-varying. Then, leveraging the monotonicity of inverse operators and the spectral decomposition of compact operators, and introducing the RKHS persistence of excitation condition, we develop a dominated convergence method to prove the mean square and almost sure consistency between the regularization path and the unknown function to be learned. Especially, for independent and non-identically distributed data streams, the mean square and almost sure consistency between the algorithm's output and the unknown function is achieved if the input data's marginal probability measures are slowly time-varying and the average measure over each fixed-length time period is uniformly above a strictly positive finite Borel measure.

cs.LG

Reflective Policy Optimization

On-policy reinforcement learning methods, like Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), often demand extensive data per update, leading to sample inefficiency. This paper introduces Reflective Policy Optimization (RPO), a novel on-policy extension that amalgamates past and future state-action information for policy optimization. This approach empowers the agent for introspection, allowing modifications to its actions within the current state. Theoretical analysis confirms that policy performance is monotonically improved and contracts the solution space, consequently expediting the convergence procedure. Empirical results demonstrate RPO's feasibility and efficacy in two reinforcement learning benchmarks, culminating in superior sample efficiency. The source code of this work is available at https://github.com/Edgargan/RPO.

cs.LG

Transductive Off-policy Proximal Policy Optimization

Proximal Policy Optimization (PPO) is a popular model-free reinforcement learning algorithm, esteemed for its simplicity and efficacy. However, due to its inherent on-policy nature, its proficiency in harnessing data from disparate policies is constrained. This paper introduces a novel off-policy extension to the original PPO method, christened Transductive Off-policy PPO (ToPPO). Herein, we provide theoretical justification for incorporating off-policy data in PPO training and prudent guidelines for its safe application. Our contribution includes a novel formulation of the policy improvement lower bound for prospective policies derived from off-policy data, accompanied by a computationally efficient mechanism to optimize this bound, underpinned by assurances of monotonic improvement. Comprehensive experimental results across six representative tasks underscore ToPPO's promising performance.

cs.LG