ReJump: A Tree-Jump Representation for Analyzing and Improving LLM Reasoning

Large Reasoning Models (LRMs) are Large Language Models (LLMs) explicitly trained to generate long-form Chain-of-Thoughts (CoTs), achieving impressive success on challenging tasks like math and programming. However, their underlying reasoning "algorithms" remain poorly understood. To investigate this, we propose ReJump, which represents a reasoning trace as a visitation order over nodes in a tree of intermediate problem-solving steps. Transitions between nodes, which we term jumps, include adjacent moves that capture behaviors such as calculation, and non-adjacent moves that capture behaviors such as backtracking and verification. ReJump enables analyzing LLM reasoning with diverse metrics that quantify exploration, exploitation, overthinking, forgetting, and verification. Using our proposed LLM agent to extract reasoning traces into ReJump format, we evaluate state-of-the-art LRMs on two tasks and find that models with similar accuracy can exhibit distinct reasoning behaviors, while different tasks favor different reasoning styles (e.g., varying balance between exploration and exploitation). To further understand how learning strategies shape reasoning, we use ReJump to compare distilled LRMs with their teachers, compare CoT-prompted LLMs with LRMs, and examine how reinforcement learning affects reasoning behavior. Finally, we show that ReJump can improve reasoning quality at test time through strategies such as ReJump-guided Best-of-N selection and prompt selection. Our code is available at https://github.com/UW-Madison-Lee-Lab/ReJump.

Large reasoning models often produce long chain-of-thought explanations, but it is hard to tell what reasoning strategy they actually use. ReJump turns each reasoning trace into movements through a tree of intermediate problem-solving steps, making it possible to measure when a model explores alternatives, commits to a path, backtracks, verifies, forgets, or overthinks. The paper uses this representation to compare modern reasoning models across tasks and training strategies, and shows that ReJump can also guide better test-time choices such as selecting among multiple generated solutions or prompts.