# CAMEx: Curvature-aware Merging of Experts

arXiv: https://arxiv.org/abs/2502.18821 · HTML: https://mlsanity.com/paper/2502.18821/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 72 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 30 of 51)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [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)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)

## Built on by (most cited first, 5 of 5)

- [REAM: Merging Improves Pruning of Experts in LLMs](https://mlsanity.com/paper/2604.04356/) (2026)
- [MoLEx: Mixture of Layer Experts for Finetuning with Sparse Upcycling](https://mlsanity.com/paper/2503.11144/) (2025)
- [Expert Merging in Sparse Mixture of Experts with Nash Bargaining](https://mlsanity.com/paper/2510.16138/) (2025)
- [Beyond Global Routing Aggregation: Phase-Aware Expert Merging for MoE Vision-Language Models](https://mlsanity.com/paper/2608.04454/) (2026)
- [SLEM: Spectrum-Aware Latent Expert Merging](https://mlsanity.com/paper/2610.16484/) (2026)

## Abstract (arXiv)

Existing methods for merging experts during model training and fine-tuning predominantly rely on Euclidean geometry, which assumes a flat parameter space. This assumption can limit the model's generalization ability, especially during the pre-training phase, where the parameter manifold might exhibit more complex curvature. Curvature-aware merging methods typically require additional information and computational resources to approximate the Fisher Information Matrix, adding memory overhead. In this paper, we introduce CAMEx (Curvature-Aware Merging of Experts), a novel expert merging protocol that incorporates natural gradients to account for the non-Euclidean curvature of the parameter manifold. By leveraging natural gradients, CAMEx adapts more effectively to the structure of the parameter space, improving alignment between model updates and the manifold's geometry. This approach enhances both pre-training and fine-tuning, resulting in better optimization trajectories and improved generalization without the substantial memory overhead typically associated with curvature-aware methods. Our contributions are threefold: (1) CAMEx significantly outperforms traditional Euclidean-based expert merging techniques across various natural language processing tasks, leading to enhanced performance during pre-training and fine-tuning; (2) we introduce a dynamic merging architecture that optimizes resource utilization, achieving high performance while reducing computational costs, facilitating efficient scaling of large language models; and (3) we provide both theoretical and empirical evidence to demonstrate the efficiency of our proposed method. The code is publicly available at: https://github.com/kpup1710/CAMEx.