Neural networks as a machine learning technique are increasingly deployed in various domains. Despite their performance and their continuous improvement, the deployment of neural networks in safety-critical systems, in particular for autonomous mobility, remains restricted. This is mainly due to the lack of (formal) specifications and verification methods and tools that allow for having sufficient confidence in the behavior of the neural-network-based functions. Recent years have seen neural network verification getting more attention; many verification methods were proposed, yet the practical applicability of these methods to real-world neural network models remains limited. The main challenge of neural network verification methods is related to the computational complexity and the large size of neural networks pertaining to complex functions. As a consequence, applying abstraction methods for neural network verification purposes is seen as a promising mean to cope with such issues. The aim of abstraction is to build an abstract model by omitting some irrelevant details or some details that are not highly impacting w.r.t some considered features. Thus, the verification process is made faster and easier while preserving, to some extent, the relevant behavior regarding the properties to be examined on the original model. In this article, we review both the abstraction techniques for activation functions and model size reduction approaches, with a particular focus on the latter. The review primarily discusses the application of abstraction techniques on feed-forward neural networks and explores the potential for applying abstraction to other types of neural networks. Throughout the article, we present the main idea of each approach and then discuss its respective advantages and limitations in detail. Finally, we provide some insights and guidelines to improve the discussed methods.

Neural networks (NNs) have witnessed widespread deployment across various domains, including some safetycritical applications. In this regard, the demand for verifying means of such artificial intelligence techniques is more and more pressing. Nowadays, the development of evaluation approaches for NNs is a hot topic that is attracting considerable interest, and a number of verification methods have been proposed. Yet, a challenging issue for NN verification is pertaining to the scalability when some NNs of practical interest have to be evaluated. This work aims to present INNAbstract, an abstraction method to reduce the size of NNs, which leads to improving the scalability of NN verification and reachability analysis methods. This is achieved by merging neurons while ensuring that the obtained model (i.e., abstract model) overapproximates the original one. INNAbstract supports networks with numerous activation functions. In addition, we propose a heuristic for nodes' selection to build more precise abstract models, in the sense that the outputs are closer to those of the original network. The experimental results illustrate the efficiency of the proposed approach compared to the existing relevant abstraction techniques. Furthermore, they demonstrate that INNAbstract can help the existing verification tools to be applied on larger networks while considering various activation functions.

This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main strength of interval-based reachability analysis is its simplicity and scalability, rather than the accuracy of the over-approximations. The current implementation of TIRA contains four reachability methods covering wide classes of nonlinear systems, handled with recent results relying on contraction/growth bounds and monotonicity concepts. TIRA's architecture features a central function working as a hub between the user-defined reachability problem and the library of available reachability methods. This design choice offers increased extensibility of the library, where users can define their own method in a separate function and add the function call in the hub function.

We describe an application of symbolic control to ventilation regulation in buildings. The monotonicity property of a nonlinear control system subject to disturbances, modeling the process, is exploited to obtain symbolic abstractions, in the sense of alternating simulation. The resulting abstractions consist of non-deterministic finite transition systems, for which we can synthesize supervisory safety controllers to keep the room temperatures within prescribed bounds. To choose among possible control inputs preserving safety, we consider the problem of minimizing a given cost function and apply a receding horizon control scheme. The approach has been applied to temperature regulation on a small-scale building equipped with underfloor air distribution (UFAD). To the best of our knowledge, this is the first report of experimental implementation of symbolic controllers.