# QA-Merging: Query-Adaptive Reasoning via Layer Selective Model Merging

arXiv: https://arxiv.org/abs/2601.03506 · HTML: https://mlsanity.com/paper/2601.03506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 32 of its 62 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.19470/) (2025)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Tasks](https://mlsanity.com/paper/2502.08235/) (2025)
- [Agentic Reasoning: A Streamlined Framework for Enhancing LLM Reasoning with Agentic Tools](https://mlsanity.com/paper/2502.04644/) (2025)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?](https://mlsanity.com/paper/2504.06514/) (2025)
- [Long-Short Chain-of-Thought Mixture Supervised Fine-Tuning Eliciting Efficient Reasoning in Large Language Models](https://mlsanity.com/paper/2505.03469/) (2025)
- [ARM: Adaptive Reasoning Model](https://mlsanity.com/paper/2505.20258/) (2025)
- [Optimizing Length Compression in Large Reasoning Models](https://mlsanity.com/paper/2506.14755/) (2025)
- [Ada-R1: Hybrid-CoT via Bi-Level Adaptive Reasoning Optimization](https://mlsanity.com/paper/2504.21659/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [Activation-Informed Merging of Large Language Models](https://mlsanity.com/paper/2502.02421/) (2025)
- [Towards Reasoning Ability of Small Language Models](https://mlsanity.com/paper/2502.11569/) (2025)
- [HAPO: Training Language Models to Reason Concisely via History-Aware Policy Optimization](https://mlsanity.com/paper/2505.11225/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [Activation-Guided Consensus Merging for Large Language Models](https://mlsanity.com/paper/2505.14009/) (2025)
- [Revisiting Model Interpolation for Efficient Reasoning](https://mlsanity.com/paper/2510.10977/) (2025)
- [When Can Large Reasoning Models Save Thinking? Mechanistic Analysis of Behavioral Divergence in Reasoning](https://mlsanity.com/paper/2505.15276/) (2025)

## Built on by (most cited first, 1 of 1)

- [Federation over Text: Insight Sharing for Multi-Agent Reasoning](https://mlsanity.com/paper/2604.16778/) (2026)

## Abstract (arXiv)

Recent large reasoning models (LRMs) have achieved strong performance on complex reasoning tasks by generating a long chain-of-thought (Long-CoT). However, such lengthy reasoning is often unnecessary for simple queries, leading to additional computation and latency. Existing approaches to adaptive reasoning typically rely on retraining the model or designing sophisticated prompting, which are either prohibitively expensive or highly sensitive to the prompt formulation. Model merging provides a more balanced alternative for adaptive reasoning by avoiding expensive training and integrating Long-CoT and Short-CoT behaviors. However, existing merging methods are often static and input-agnostic, or rely on costly all-layer calibration, which limits their effectiveness for query-adaptive reasoning. To tackle these challenges, we propose Query-adaptive Layer Selective Merging (QA-Merging), an activation-based merging framework that integrates a Long-CoT model and a Short-CoT model to obtain a query-adaptive reasoner without training from scratch or requiring large-scale additional data. QA-Merging first constructs a small pattern-labeled calibration set that assigns each query an appropriate reasoning pattern. Motivated by our empirical analysis that Long-CoT and Short-CoT behaviors diverge unevenly across transformer layers, QA-Merging identifies layers with high reasoning pattern divergence and calibrates only these layers through feature alignment and contrastive shaping, while applying closed-form hidden-state correction to the remaining layers. Experiments on seven widely used reasoning benchmarks across two model scales demonstrate that QA-Merging reduces inference cost and maintains strong performance.