# RegMean++: Enhancing Effectiveness and Generalization of Regression Mean for Model Merging

arXiv: https://arxiv.org/abs/2508.03121 · HTML: https://mlsanity.com/paper/2508.03121/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 77 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 30 of 54)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (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)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- ["Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models](https://mlsanity.com/paper/2308.03825/) (2023)

## Built on by (most cited first, 11 of 11)

- [ACE-Merging: Data-Free Model Merging with Adaptive Covariance Estimation](https://mlsanity.com/paper/2603.02945/) (2026)
- [FeatCal: Feature Calibration for Post-Merging Models](https://mlsanity.com/paper/2605.13030/) (2026)
- [Compress then Merge: From Multiple LoRAs into One Low-Rank Adapter](https://mlsanity.com/paper/2606.03723/) (2026)
- [Model Merging via Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2512.21288/) (2025)
- [PACT: Preserving Anchored Cores in Task-vectors for Model Merging](https://mlsanity.com/paper/2606.18627/) (2026)
- [Exploring Information Seeking Agent Consolidation](https://mlsanity.com/paper/2602.00585/) (2026)
- [LARV: Data-Free Layer-wise Adaptive Rescaling Veneer for Model Merging](https://mlsanity.com/paper/2602.09413/) (2026)
- [The Mean is the Mirage: Entropy-Adaptive Model Merging under Heterogeneous Domain Shifts in Medical Imaging](https://mlsanity.com/paper/2602.21372/) (2026)
- [CoMerge: Conflict-Driven Preference Optimization for Multi-Task Model Merging](https://mlsanity.com/paper/2609.02273/) (2026)
- [Tracing and Coordinating Cross-Layer Influence for Multimodal Model Merging](https://mlsanity.com/paper/2609.12897/) (2026)
- [CrossMean: Model Merging by Pairing Merged and Expert Activations](https://mlsanity.com/paper/2610.14762/) (2026)

## Abstract (arXiv)

Regression Mean (RegMean), an approach that formulates model merging as a linear regression problem, aims to find the optimal weights for each linear layer in the merged model by minimizing the discrepancy in predictions between the merged and candidate models. RegMean provides a precise closed-form solution for the merging problem; therefore, it offers explainability and computational efficiency. However, RegMean merges each linear layer independently, overlooking how the features and information in earlier layers propagate through deeper layers and influence the final predictions of the merged model. Here, we introduce RegMean++, a simple yet effective alternative to RegMean, that explicitly incorporates both intra-layer and cross-layer dependencies between merged models' layers into RegMean's objective. By accounting for these dependencies, RegMean++ better captures the behaviors of the merged model. Extensive experiments demonstrate that RegMean++ consistently outperforms RegMean across diverse settings, including in-domain (ID) and out-of-domain (OOD) generalization, sequential merging, large-scale tasks, and robustness under several types of distribution shifts. Furthermore, RegMean++ achieves competitive performance across diverse settings compared to various advanced model merging methods.