Exploring the Manifold of Neural Networks Using Diffusion Geometry
This work provides a method for analyzing neural network spaces to improve optimization tasks, but it is incremental as it applies existing manifold learning techniques to a new context.
The authors tackled the problem of understanding the structure of neural network spaces by applying manifold learning to create a low-dimensional representation, revealing that high-performing networks cluster together consistently. They demonstrated its utility for hyperparameter optimization and neural architecture search by sampling from this manifold.
Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.