Towards rigorous understanding of neural networks via semantics-preserving transformations
-
Published:2023-05-30
Issue:3
Volume:25
Page:301-327
-
ISSN:1433-2779
-
Container-title:International Journal on Software Tools for Technology Transfer
-
language:en
-
Short-container-title:Int J Softw Tools Technol Transfer
Author:
Schlüter Maximilian,Nolte Gerrit,Murtovi Alnis,Steffen Bernhard
Abstract
AbstractIn 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.
Funder
Technische Universität Dortmund
Publisher
Springer Science and Business Media LLC
Subject
Information Systems,Software
Reference63 articles.
1. Arora, R., Basu, A., Mianjy, P., Mukherjee, A.: Understanding deep neural networks with rectified linear units. arXiv preprint (2016). arXiv:1611.01491 2. Axler, S.: Linear Algebra Done Right. Springer, Berlin (1997) 3. Bach, S., Binder, A., Montavon, G., Klauschen, F., Müller, K.R., Samek, W.: On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLoS ONE 10(7), e0130140 (2015) 4. Badue, C., Guidolini, R., Carneiro, R.V., Azevedo, P., Cardoso, V.B., Forechi, A., Jesus, L., Berriel, R., Paixao, T.M., Mutz, F., et al.: Self-driving cars: a survey. Expert Syst. Appl. 165, 113816 (2021) 5. Bahar, R.I., Frohm, E.A., Gaona, C.M., Hachtel, G.D., Macii, E., Pardo, A., Somenzi, F.: Algebric decision diagrams and their applications. Form. Methods Syst. Des. 10(2), 171–206 (1997)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Explanation Paradigms Leveraging Analytic Intuition (ExPLAIn);International Journal on Software Tools for Technology Transfer;2023-06 2. Forest GUMP: a tool for verification and explanation;International Journal on Software Tools for Technology Transfer;2023-05-30 3. The power of typed affine decision structures: a case study;International Journal on Software Tools for Technology Transfer;2023-04-21
|
|