Computer Science > Neural and Evolutionary Computing
[Submitted on 19 Jan 2023 (v1), last revised 28 Apr 2023 (this version, v2)]
Title:Towards Rigorous Understanding of Neural Networks via Semantics-preserving Transformations
View PDFAbstract:In this paper we present an algebraic approach to the precise and global verification and explanation of Rectifier Neural Networks, a subclass of Piece-wise Linear Neural Networks (PLNNs), i.e., networks that semantically represent piece-wise affine functions. Key to our approach is the symbolic execution of these networks that allows the construction of semantically equivalent Typed Affine Decision Structures (TADS). Due to their deterministic and sequential nature, TADS can, similarly to decision trees, be considered as white-box models and therefore as precise solutions to the model and outcome explanation problem. TADS are linear algebras which allows one to elegantly compare Rectifier Networks for equivalence or similarity, both with precise diagnostic information in case of failure, and to characterize their classification potential by precisely characterizing the set of inputs that are specifically classified or the set of inputs where two network-based classifiers differ. All phenomena are illustrated along a detailed discussion of a minimal, illustrative example: the continuous XOR function.
Submission history
From: Gerrit Nolte [view email][v1] Thu, 19 Jan 2023 11:35:07 UTC (2,430 KB)
[v2] Fri, 28 Apr 2023 15:00:01 UTC (2,438 KB)
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