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Exact Preimages of Neural Network Aircraft Collision Avoidance Systems
Kyle Matoba · François Fleuret

A common pattern of progress in engineering has seen deep neural networks displacing human-designed logic. There are many advantages to this approach, divorcing decisionmaking from human oversight and intuition has costs as well. One is that deep neural networks can map similar inputs to very different outputs in a way that makes their application to safety-critical problem problematic.

We present a method to check that the decisions of a deep neural network are as intended by constructing the exact preimage of its predictions. Preimages generalize verification in the sense that they can be used to verify a wide class of properties, and answer much richer questions besides. We examine the functioning of an aircraft collision avoidance system, and show how exact preimages reduce undue conservatism when examining dynamic safety.

Our method iterates backwards through the layers of piecewise linear deep neural networks. Uniquely, we compute \emph{all} intermediate values that correspond to a prediction, propagating this calculation through layers using analytical formulae for layer preimages.

Author Information

Kyle Matoba (EPFL)
François Fleuret (University of Geneva)

François Fleuret got a PhD in Mathematics from INRIA and the University of Paris VI in 2000, and an Habilitation degree in Mathematics from the University of Paris XIII in 2006. He is Full Professor in the department of Computer Science at the University of Geneva, and Adjunct Professor in the School of Engineering of the École Polytechnique Fédérale de Lausanne. He has published more than 80 papers in peer-reviewed international conferences and journals. He is Associate Editor of the IEEE Transactions on Pattern Analysis and Machine Intelligence, serves as Area Chair for NeurIPS, AAAI, and ICCV, and in the program committee of many top-tier international conferences in machine learning and computer vision. He was or is expert for multiple funding agencies. He is the inventor of several patents in the field of machine learning, and co-founder of Neural Concept SA, a company specializing in the development and commercialization of deep learning solutions for engineering design. His main research interest is machine learning, with a particular focus on computational aspects and sample efficiency.

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