# Merging Models with Fisher-Weighted Averaging

arXiv: https://arxiv.org/abs/2111.09832 · HTML: https://mlsanity.com/paper/2111.09832/

## Key facts

- Cited by 621 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 73 references that are in the map.
- First posted on arXiv 18 Nov 2021.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Multi-Task Identification of Entities, Relations, and Coreference for Scientific Knowledge Graph Construction](https://mlsanity.com/paper/1808.09602/) (2018)
- [Caffe: Convolutional Architecture for Fast Feature Embedding](https://mlsanity.com/paper/1408.5093/) (2014)

## Built on by (most cited first, 30 of 621)

- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [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)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [VQGAN-CLIP: Open Domain Image Generation and Editing with Natural Language Guidance](https://mlsanity.com/paper/2204.08583/) (2022)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Composing Parameter-Efficient Modules with Arithmetic Operations](https://mlsanity.com/paper/2306.14870/) (2023)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Towards Safer Large Language Models through Machine Unlearning](https://mlsanity.com/paper/2402.10058/) (2024)
- [AdaMix: Mixture-of-Adaptations for Parameter-efficient Model Tuning](https://mlsanity.com/paper/2210.17451/) (2022)
- [Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks](https://mlsanity.com/paper/2312.06795/) (2023)
- [Localizing Task Information for Improved Model Merging and Compression](https://mlsanity.com/paper/2405.07813/) (2024)
- [LaCo: Large Language Model Pruning via Layer Collapse](https://mlsanity.com/paper/2402.11187/) (2024)
- [MiniCache: KV Cache Compression in Depth Dimension for Large Language Models](https://mlsanity.com/paper/2405.14366/) (2024)
- [Safe LoRA: the Silver Lining of Reducing Safety Risks when Fine-tuning Large Language Models](https://mlsanity.com/paper/2405.16833/) (2024)
- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging](https://mlsanity.com/paper/2406.15479/) (2024)
- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)

## Abstract (arXiv)

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.