# Reasoning Relay: Evaluating Stability and Interchangeability of Large Language Models in Mathematical Reasoning

arXiv: https://arxiv.org/abs/2512.20647 · HTML: https://mlsanity.com/paper/2512.20647/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 23 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Q*: Improving Multi-step Reasoning for LLMs with Deliberative Planning](https://mlsanity.com/paper/2406.14283/) (2024)
- [Prompt Design and Engineering: Introduction and Advanced Methods](https://mlsanity.com/paper/2401.14423/) (2024)
- [Direct Evaluation of Chain-of-Thought in Multi-hop Reasoning with Knowledge Graphs](https://mlsanity.com/paper/2402.11199/) (2024)
- [LogiCoT: Logical Chain-of-Thought Instruction-Tuning](https://mlsanity.com/paper/2305.12147/) (2023)
- [Zero-Shot Chain-of-Thought Reasoning Guided by Evolutionary Algorithms in Large Language Models](https://mlsanity.com/paper/2402.05376/) (2024)
- [United Minds or Isolated Agents? Exploring Coordination of LLMs under Cognitive Load Theory](https://mlsanity.com/paper/2506.06843/) (2025)

## Built on by (most cited first, 2 of 2)

- [Probing the Trajectories of Reasoning Traces in Large Language Models](https://mlsanity.com/paper/2601.23163/) (2026)
- [What Does a Token Cost? A Mixture-of-Agents Measurement of Sufficient Per-Token Compute](https://mlsanity.com/paper/2610.02491/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of large language models (LLMs). While prior work focuses on improving model performance through internal reasoning strategies, little is known about the interchangeability of reasoning across different models. In this work, we explore whether a partially completed reasoning chain from one model can be reliably continued by another model, either within the same model family or across families. We achieve this by assessing the sufficiency of intermediate reasoning traces as transferable scaffolds for logical coherence and final answer accuracy. We interpret this interchangeability as a means of examining inference-time trustworthiness, probing whether reasoning remains both coherent and reliable under model substitution. Using token-level log-probability thresholds to truncate reasoning at early, mid, and late stages from our baseline models, Gemma-3-4B-IT and LLaMA-3.1-70B-Instruct, we conduct continuation experiments with Gemma-3-1B-IT and LLaMA-3.1-8B-Instruct to test intra-family and cross-family behaviors. Our evaluation pipeline leverages truncation thresholds with a Process Reward Model (PRM), providing a reproducible framework for assessing reasoning stability via model interchange. Evaluations with a PRM reveal that hybrid reasoning chains often preserve, and in some cases even improve, final accuracy and logical structure. Our findings point towards interchangeability as an emerging behavioral property of reasoning models, offering insights into new paradigms for reliable modular reasoning in collaborative AI systems.