Exploring the Manifold of Neural Networks Using Diffusion Geometry

TL;DR

This paper applies diffusion geometry and manifold learning to the space of neural networks, revealing structures that correlate with performance and aiding hyperparameter and architecture optimization.

Contribution

It introduces a novel manifold learning approach for neural networks using diffusion geometry and PHATE, enabling analysis and sampling of network spaces.

Findings

High-performing networks cluster together in the manifold

Manifold features correlate with network performance

Sampling from the manifold can guide hyperparameter tuning

Abstract

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.