# Mode Combinability: Exploring Convex Combinations of Permutation Aligned Models

arXiv: https://arxiv.org/abs/2308.11511 · HTML: https://mlsanity.com/paper/2308.11511/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 23 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Model Fusion via Optimal Transport](https://mlsanity.com/paper/1910.05653/) (2019)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [REPAIR: REnormalizing Permuted Activations for Interpolation Repair](https://mlsanity.com/paper/2211.08403/) (2022)
- [Similarity and Matching of Neural Network Representations](https://mlsanity.com/paper/2110.14633/) (2021)

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

- [DIMAT: Decentralized Iterative Merging-And-Training for Deep Learning Models](https://mlsanity.com/paper/2404.08079/) (2024)

## Abstract (arXiv)

We explore element-wise convex combinations of two permutation-aligned neural network parameter vectors ThetaA and ThetaB of size d. We conduct extensive experiments by examining various distributions of such model combinations parametrized by elements of the hypercube [0,1]d and its vicinity. Our findings reveal that broad regions of the hypercube form surfaces of low loss values, indicating that the notion of linear mode connectivity extends to a more general phenomenon which we call mode combinability. We also make several novel observations regarding linear mode connectivity and model re-basin. We demonstrate a transitivity property: two models re-based to a common third model are also linear mode connected, and a robustness property: even with significant perturbations of the neuron matchings the resulting combinations continue to form a working model. Moreover, we analyze the functional and weight similarity of model combinations and show that such combinations are non-vacuous in the sense that there are significant functional differences between the resulting models.