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About this paper
Frederik Benzing, Simon Schug, Robert Meier, Johannes von Oswald, Yassir Akram, Nicolas Zucchet, Laurence Aitchison, Angelika Steger
The authors test whether activation-based matching of hidden units can align independently trained neural networks for weight interpolation. Their heuristic matches units by activation similarity and reorders adjacent weights, preserving each network’s function. In fully connected Fashion-MNIST networks, permutations learned from trained copies also make averaged untrained initializations achieve accuracy above chance; tested CNNs retain barriers.
Key insights
- Permutation invariance is crucial for understanding the connectivity of neural network loss landscapes, significantly reducing loss barriers, especially in wide fully connected networks.
- For fully connected networks, the property of residing in a shared loss valley (up to permutation) is present at random initialization, suggesting an inherent architectural inductive bias.
- The loss landscape properties, including solution diversity and mode connectivity, vary substantially between fully connected and convolutional networks and are highly sensitive to training hyperparameters like the learning rate.
Summary by alphaXiv.
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