Reachability in Simple Neural Networks

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Marco Sälzer, Martin Lange
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引用次数: 0

Abstract

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.
简单神经网络的可达性
我们研究了(深度)神经网络可达性问题的复杂性:它是否在给定有效输入的情况下计算有效输出?最近有人声称,对于一般神经网络来说,这个问题是np完全的,并且对线性不等式的连接给出的输入/输出维进行了规范。我们对证明进行了概括,并对原上界和下界证明中的一些缺陷进行了修正。在一般结果的激励下,我们表明np -硬度已经适用于简单规范和神经网络的限制类。允许单个隐藏层和输出维度为1,以及只有一个负、零和一个正权重或偏差的神经网络,足以确保np硬度。此外,我们还对神经网络验证这一研究方向的可能扩展进行了深入的讨论和展望。
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来源期刊
Fundamenta Informaticae
Fundamenta Informaticae 工程技术-计算机:软件工程
CiteScore
2.00
自引率
0.00%
发文量
61
审稿时长
9.8 months
期刊介绍: Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.
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