# ResMerge: Residual-based Spectral Merging of Large Language Models

arXiv: https://arxiv.org/abs/2606.02252 · HTML: https://mlsanity.com/paper/2606.02252/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces](https://mlsanity.com/paper/2502.04959/) (2025)
- [WARP: On the Benefits of Weight Averaged Rewarded Policies](https://mlsanity.com/paper/2406.16768/) (2024)
- [LiNeS: Post-training Layer Scaling Prevents Forgetting and Enhances Model Merging](https://mlsanity.com/paper/2410.17146/) (2024)
- [STAR: Spectral Truncation and Rescale for Model Merging](https://mlsanity.com/paper/2502.10339/) (2025)
- [Behavior Knowledge Merge in Reinforced Agentic Models](https://mlsanity.com/paper/2601.13572/) (2026)
- [AdaRank: Adaptive Rank Pruning for Enhanced Model Merging](https://mlsanity.com/paper/2503.22178/) (2025)
- [When Shared Knowledge Hurts: Spectral Over-Accumulation in Model Merging](https://mlsanity.com/paper/2602.05536/) (2026)
- [SALSA: Soup-based Alignment Learning for Stronger Adaptation in RLHF](https://mlsanity.com/paper/2411.01798/) (2024)

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

- [Does Scaling Reinforcement Learning Really Require More Training?](https://mlsanity.com/paper/2610.01133/) (2026)

## Abstract (arXiv)

Model merging offers a training-free way to combine multiple post-trained expert models, but merging experts obtained through reinforcement learning (RL) remains challenging. Existing spectral merging methods often assume that leading singular directions contain the main task signal, while lower-energy residual components can be compressed, selected, or attenuated to reduce interference. We find that this assumption does not hold for RL task vectors: after decomposing each task vector into a leading spectral head and a residual component, both parts can independently recover substantial behavior knowledge, while exhibiting different merging properties. The head is highly concentrated and informative but more prone to sharp cross-expert conflicts, whereas the residual component is more dispersed and provides a more stable basis for aggregation. Based on this observation, we propose ResMerge, a residual-based spectral merging framework for RL experts. ResMerge first constructs a stable residual backbone with Spherical Residual Consensus Adaptation, which estimates a reliability-weighted consensus direction on the Frobenius sphere. It then reintroduces leading-head information through a Lightweight Head Correction module gated by positive cross-expert agreement. Experiments across multiple RL expert groups and capability domains show that ResMerge better preserves expert capabilities than representative task-vector and spectral merging baselines.