2022/12/03 by Joshua Pilipovsky, Pilipovsky, Joshua, Vignesh Sivaramakrishnan +5 · 2 citations
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Neural Networks and Applications #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2212.01544
openalex publication_date 2022/12/03 · openalex created_date 2022/12/18 · openalex updated_date 2026/07/28
Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use ideas from probability theory in the frequency domain to provide probabilistic verification guarantees for ReLU neural networks. Specifically, we interpret a (deep) feedforward neural network as a discrete dynamical system over a finite horizon that shapes distributions of initial states, and use characteristic functions to propagate the distribution of the input data through the network. Using the inverse Fourier transform, we obtain the corresponding cumulative distribution function of the output set, which can be used to check if the network is performing as expected given any random point from the input set. The proposed approach does not require distributions to have well-defined moments or moment generating functions. We demonstrate our proposed approach on two examples, and compare its performance to related approaches.