Towards rigorous understanding of neural networks via semantics-preserving transformations

Abstract In this paper, we present an algebraic approach to the precise and global verification explanation of Rectifier Neural Networks , a subclass Piece-wise Linear (PLNNs), i.e., networks that semantically represent piece-wise affine functions. Key our is symbolic execution these allows construction equivalent Typed Affine Decision Structures (TADS). Due their deterministic sequential nature, TADS can, similarly decision trees, be considered as white-box models therefore solutions model outcome problem. are linear algebras, which one elegantly compare for equivalence or similarity, both with diagnostic information in case failure, characterize classification potential by precisely characterizing set inputs specifically classified, where two network-based classifiers differ. All phenomena illustrated along detailed discussion minimal, illustrative example: continuous XOR function.