# RAIN-Merging: A Gradient-Free Method to Enhance Instruction Following in Large Reasoning Models with Preserved Thinking Format

arXiv: https://arxiv.org/abs/2602.22538 · HTML: https://mlsanity.com/paper/2602.22538/

## Key facts

- Cited by 9 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 28 of its 78 references that are in the map.
- First posted on arXiv 26 Feb 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, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Revolutionizing Finance with LLMs: An Overview of Applications and Insights](https://mlsanity.com/paper/2401.11641/) (2024)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [When Thinking Fails: The Pitfalls of Reasoning for Instruction-Following in LLMs](https://mlsanity.com/paper/2505.11423/) (2025)
- [AGENTIF: Benchmarking Instruction Following of Large Language Models in Agentic Scenarios](https://mlsanity.com/paper/2505.16944/) (2025)
- [LLMs are Greedy Agents: Effects of RL Fine-tuning on Decision-Making Abilities](https://mlsanity.com/paper/2504.16078/) (2025)
- [Activation-Informed Merging of Large Language Models](https://mlsanity.com/paper/2502.02421/) (2025)
- [Scaling Reasoning, Losing Control: Evaluating Instruction Following in Large Reasoning Models](https://mlsanity.com/paper/2505.14810/) (2025)
- [Incentivizing Reasoning for Advanced Instruction-Following of Large Language Models](https://mlsanity.com/paper/2506.01413/) (2025)
- [Put the Space of LoRA Initialization to the Extreme to Preserve Pre-trained Knowledge](https://mlsanity.com/paper/2503.02659/) (2025)
- [Joint Evaluation of Answer and Reasoning Consistency for Hallucination Detection in Large Reasoning Models](https://mlsanity.com/paper/2506.04832/) (2025)
- [Activation-Guided Consensus Merging for Large Language Models](https://mlsanity.com/paper/2505.14009/) (2025)
- [Step Guided Reasoning: Improving Mathematical Reasoning using Guidance Generation and Step Reasoning](https://mlsanity.com/paper/2410.19817/) (2024)
- [Instruction Following by Principled Boosting Attention of Large Language Models](https://mlsanity.com/paper/2506.13734/) (2025)
- [LEWIS (LayEr WIse Sparsity) -- A Training Free Guided Model Merging Approach](https://mlsanity.com/paper/2503.03874/) (2025)

## Built on by (most cited first, 9 of 9)

- [M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models](https://mlsanity.com/paper/2605.09879/) (2026)
- [PaperFit: Vision-in-the-Loop Typesetting Optimization for Scientific Documents](https://mlsanity.com/paper/2605.10341/) (2026)
- [Reading the Gate, Not the Interference: Output-Side Interference Measurement Does Not Track Merge Collapse](https://mlsanity.com/paper/2608.11797/) (2026)
- [CRANE: Constrained Reasoning Injection for Code Agents via Nullspace Editing](https://mlsanity.com/paper/2605.14084/) (2026)
- [Towards Efficient Reasoning in LLM-Based Recommender Systems via Model Merging](https://mlsanity.com/paper/2608.10447/) (2026)
- [MergeHEIR: Mitigating Multimodal Hallucinations as the Tax of Model Merging](https://mlsanity.com/paper/2609.32422/) (2026)
- [Mixture-Trained Merging for Unified Multi-Objective Models](https://mlsanity.com/paper/2610.01238/) (2026)
- [Predicting and Repairing Merge Collapse in Large Language Models](https://mlsanity.com/paper/2610.03199/) (2026)
- [UniMergeTrack: Hierarchical Model Merging for General RGB-X Visual Object Tracking](https://mlsanity.com/paper/2610.13053/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) excel at a long chain of reasoning but often fail to faithfully follow instructions regarding output format, constraints, or specific requirements. We investigate whether this gap can be closed by integrating an instruction-tuned model (ITM) into an LRM. Analyzing their differences in parameter space, namely task vectors, we find that their principal subspaces are nearly orthogonal across key modules, suggesting a lightweight merging with minimal interference. However, we also demonstrate that naive merges are fragile because they overlook the output format mismatch between LRMs (with explicit thinking and response segments) and ITMs (answers-only). We introduce RAIN-Merging (Reasoning-Aware Instruction-attention guided Null-space projection Merging), a gradient-free method that integrates instruction following while preserving thinking format and reasoning performance. First, with a small reasoning calibration set, we project the ITM task vector onto the null space of forward features at thinking special tokens, which preserves the LRM's structured reasoning mechanisms. Second, using a small instruction calibration set, we estimate instruction attention to derive module-specific scaling that amplifies instruction-relevant components and suppresses leakage. Across four instruction-following benchmarks and nine reasoning & general capability benchmarks, RAIN-Merging substantially improves instruction adherence while maintaining reasoning quality. The gains are consistent across model scales and architectures, translating to improved performance in agent settings.