



01719nas a2200121   4500008004100000245006500041210006500106260001300171520132800184100002501512700002301537856003701560       2019                        eng d00aInvestigating Decision Boundaries of Trained Neural Networks0 aInvestigating Decision Boundaries of Trained Neural Networks  c8/7/20193 a<p>Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision boundaries, and therefore, many of the studies about deep learning models speculate about the decision boundaries, and sometimes make simplifying assumptions about them. So far, finding exact points on the decision boundaries of trained deep models has been considered an intractable problem. Here, we compute exact points on the decision boundaries of these models and provide mathematical tools to investigate the surfaces that define the decision boundaries. Through numerical results, we confirm that some of the speculations about the decision boundaries are accurate, some of the computational methods can be improved, and some of the simplifying assumptions may be unreliable, for models with nonlinear activation functions. We advocate for verification of simplifying assumptions and approximation methods, wherever they are used. Finally, we demonstrate that the computational practices used for finding adversarial examples can be improved and computing the closest point on the decision boundary reveals the weakest vulnerability of a model against adversarial attack.</p>1 aYousefzadeh, Roozbeh1 aO'Leary, Dianne, P  uhttps://arxiv.org/abs/1908.02802