Principles of Deep Feedforward ReLU Networks Unveiled.

Deep feedforward neural networks, particularly those using ReLU activation functions, are fundamental to deep learning, yet their internal workings often remain opaque. This research aims to demystify these "black box" mechanisms by extending principles observed in simpler two-layer ReLU networks to more complex, multi-layered architectures. The study highlights the critical role of "paths" within the network and their interrelationships in explaining the solutions derived through the back-propagation algorithm. It demonstrates that units in deep ReLU networks create piecewise linear manifolds to partition the input space, a more complex division than the hyperplanes formed by two-layer networks. The paper also addresses how hidden-layer units efficiently generate both linear functions and input space partitions, suggesting that many core principles from simpler networks, such as strict partial orders and continuity restrictions, largely generalize to deeper configurations.