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Modeling Hierarchical Thinking in Large Reasoning Models

G M Shahariar, Ali Nazari, Erfan Shayegani, Nael Abu-Ghazaleh

TL;DR

This work investigates how large language models exhibit hierarchical reasoning when trained with chain-of-thought prompts. It introduces a memoryless finite-state machine (FSM) abstraction to represent CoT traces as transitions among six states: init, deduce, augment, uncertain, backtrack, and closure, enabling interpretable analysis through state frequencies and transition matrices. Using two benchmarks, AIME 25 and GPQA Diamond, and three open models, the study shows that longer FSM trajectories tend to align with higher accuracy on structured math tasks but not universally across domains, and that high performers combine deduction with adaptive augmentation and uncertainty handling. The FSM framework offers a practical tool for interpretability, training guidance, and robustness evaluation, with potential applications in controllability and reasoning editing across diverse reasoning tasks.

Abstract

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities when they generate step-by-step solutions, known as chain-of-thought (CoT) reasoning. When trained to using chain-of-thought reasoning examples, the resulting models (called Large Reasoning Models, or LRMs) appear to learn hierarchical thinking strategies similar to those used by humans. However, understanding LRMs emerging reasoning capabilities remains a difficult open problem, with many potential important applications including improving training and understanding robustness. In this paper, we adopt a memoryless Finite State Machine formulation to approximate LRM's emerging hierarchical reasoning dynamics as a structured, interpretable abstraction. We identify a small set of discrete reasoning states including - initialization, deduction, augmentation-strategy, uncertainty-estimation, backtracking, and final-conclusion that capture the high-level states present in the model's reasoning process. By annotating each step of a model's CoT with these states, we can represent the reasoning trajectory as a transition sequence through the state graph. This FSM formulation provides a systematic way to analyze, interpret and visualize how different models approach problems. We describe the FSM model, provide examples of CoT annotations under this scheme, and discuss how it can shed light on differences between available models in their approach to reasoning. Our results demonstrate that this FSM-based analysis reveals distinct reasoning patterns and potential shortcomings, offering a new lens to evaluate and improve LLM reasoning.

Modeling Hierarchical Thinking in Large Reasoning Models

TL;DR

This work investigates how large language models exhibit hierarchical reasoning when trained with chain-of-thought prompts. It introduces a memoryless finite-state machine (FSM) abstraction to represent CoT traces as transitions among six states: init, deduce, augment, uncertain, backtrack, and closure, enabling interpretable analysis through state frequencies and transition matrices. Using two benchmarks, AIME 25 and GPQA Diamond, and three open models, the study shows that longer FSM trajectories tend to align with higher accuracy on structured math tasks but not universally across domains, and that high performers combine deduction with adaptive augmentation and uncertainty handling. The FSM framework offers a practical tool for interpretability, training guidance, and robustness evaluation, with potential applications in controllability and reasoning editing across diverse reasoning tasks.

Abstract

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities when they generate step-by-step solutions, known as chain-of-thought (CoT) reasoning. When trained to using chain-of-thought reasoning examples, the resulting models (called Large Reasoning Models, or LRMs) appear to learn hierarchical thinking strategies similar to those used by humans. However, understanding LRMs emerging reasoning capabilities remains a difficult open problem, with many potential important applications including improving training and understanding robustness. In this paper, we adopt a memoryless Finite State Machine formulation to approximate LRM's emerging hierarchical reasoning dynamics as a structured, interpretable abstraction. We identify a small set of discrete reasoning states including - initialization, deduction, augmentation-strategy, uncertainty-estimation, backtracking, and final-conclusion that capture the high-level states present in the model's reasoning process. By annotating each step of a model's CoT with these states, we can represent the reasoning trajectory as a transition sequence through the state graph. This FSM formulation provides a systematic way to analyze, interpret and visualize how different models approach problems. We describe the FSM model, provide examples of CoT annotations under this scheme, and discuss how it can shed light on differences between available models in their approach to reasoning. Our results demonstrate that this FSM-based analysis reveals distinct reasoning patterns and potential shortcomings, offering a new lens to evaluate and improve LLM reasoning.
Paper Structure (22 sections, 2 equations, 3 figures, 2 tables)

This paper contains 22 sections, 2 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Modeling LLM Reasoning
  3. Foundation of FSM View of Reasoning
  4. FSM Formalization
  5. The State Space (Q)
  6. (1) Initialization (init).
  7. (2) Deduction (deduce).
  8. (3) Augmentation Strategy (augment).
  9. (4) Uncertainty Estimation (uncertain).
  10. (5) Backtracking (backtrack).
  11. (6) Final Conclusion (closure).
  12. Reasoning Path
  13. Transition Constraints
  14. Experimental Setup
  15. Results and Analysis
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Comparison of FSM state frequency distributions across models and datasets.
  • Figure 2: State transition (row centric) visualization across models. Top row: sentence and paragraph level transition heatmaps on AIME 25 dataset. Bottom row: sentence and paragraph level transition heatmaps on GPQA Diamond dataset.
  • Figure 3: State transition graphs across models. Top row: sentence and paragraph level transition graphs on AIME 25 dataset. Bottom row: sentence and paragraph level transition graphs on GPQA Diamond dataset. These state graphs are generated using the transition probabilities from Figure \ref{['fig:transition_viz']}. Here, I = init, D = deduce, A = augment, U = uncertain, B = backtrack, C = closure.