Summary of Simultaneous Linear Connectivity Of Neural Networks Modulo Permutation, by Ekansh Sharma et al.
Simultaneous linear connectivity of neural networks modulo permutation
by Ekansh Sharma, Devin Kwok, Tom Denton, Daniel M. Roy, David Rolnick, Gintare Karolina Dziugaite
First submitted to arxiv on: 9 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A recent study on neural networks has shown that permutation symmetries can contribute to non-convexity in the loss landscape. This work refines previous arguments into three claims: weak linear connectivity, strong linear connectivity, and intermediate alignment. Weak linear connectivity implies that each pair of networks can be connected by multiple permutations, while strong linear connectivity suggests that a single permutation connects each network with others. The study also introduces an intermediate claim, showing that a single permutation aligns sequences of iteratively trained and pruned networks. These findings have implications for model interpolation and optimization. Specifically, the authors demonstrate that barriers decrease with increasing network width when interpolating among three networks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about how neural networks work. It shows that when you move around different versions of a trained network, it can be hard to get from one version to another because of something called permutation symmetries. The authors have three main ideas: first, they show that it’s possible to connect two networks with multiple permutations. Second, they propose an idea called “strong linear connectivity” which would make it easier to move between different versions of a network. Finally, they find evidence that this strong connection is possible under certain conditions. |
Keywords
* Artificial intelligence * Alignment * Optimization
