# Soft Merging: A Flexible and Robust Soft Model Merging Approach for Enhanced Neural Network Performance

arXiv: https://arxiv.org/abs/2309.12259 · HTML: https://mlsanity.com/paper/2309.12259/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 21 Sep 2023.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Merging of neural networks](https://mlsanity.com/paper/2204.09973/) (2022)

## Abstract (arXiv)

Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance remains a challenging task. Given the inherent complexity of neural networks, the simple arithmetic averaging of the obtained local optima models in undesirable results. This paper proposes a em soft merging method that facilitates rapid merging of multiple models, simplifies the merging of specific parts of neural networks, and enhances robustness against malicious models with extreme values. This is achieved by learning gate parameters through a surrogate of the l0 norm using hard concrete distribution without modifying the model weights of the given local optima models. This merging process not only enhances the model performance by converging to a better local optimum, but also minimizes computational costs, offering an efficient and explicit learning process integrated with stochastic gradient descent. Thorough experiments underscore the effectiveness and superior performance of the merged neural networks.