Information Geometry of Evolution of Neural Network Parameters While Training
This work addresses the problem of limited interpretability in neural networks for researchers and practitioners by providing a novel analytical tool, though it appears incremental as it builds on existing information geometry methods.
The study applied an information geometric framework to analyze phase transition-like behavior during neural network training, linking these transitions to overfitting in models like MNIST, FMNIST, and CIFAR-10, and showing mathematical similarities to physical phase transitions.
Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have been proposed to enhance the explainability and interpretability of ANNs. In this study, we introduce the application of information geometric framework to investigate phase transition-like behavior during the training of ANNs and relate these transitions to overfitting in certain models. The evolution of ANNs during training is studied by looking at the probability distribution of its parameters. Information geometry utilizing the principles of differential geometry, offers a unique perspective on probability and statistics by considering probability density functions as points on a Riemannian manifold. We create this manifold using a metric based on Fisher information to define a distance and a velocity. By parameterizing this distance and velocity with training steps, we study how the ANN evolves as training progresses. Utilizing standard datasets like MNIST, FMNIST and CIFAR-10, we observe a transition in the motion on the manifold while training the ANN and this transition is identified with over-fitting in the ANN models considered. The information geometric transitions observed is shown to be mathematically similar to the phase transitions in physics. Preliminary results showing finite-size scaling behavior is also provided. This work contributes to the development of robust tools for improving the explainability and interpretability of ANNs, aiding in our understanding of the variability of the parameters these complex models exhibit during training.