Exploring the robustness spectrum of neural networks through enhanced sampling methods

Neural networks are complex systems with huge computational power whose internal dynamics is still poorly understood. The intricate relation between the statistical properties of supervised tasks they are trained on and the geometry of the resulting internal representations is an open research problem. In particular, a coarse-grained description of internal representations seems fruitful in studying their computational and generalization capabilities. In this work, we introduce a method to study the resilience of a network to neuronal death by employing the Wang Landau algorithm, a non-markovian sampling method. While such method has been used to study coarse-graining of macromolecules, it is virtually unknown to the Machine Learning and Computational Neuroscience community. Focusing on a simple data model that naturally induces a convolutional structure fully connected networks trained from scratch, we examine resilience to network attacks in relation to the amount of spatial localization of receptive fields in the fist layer. We further investigate the dynamics of the network's parameters and the features of the internal representations during training.