Are Safety Guarantees in Neural Networks Safe? How to Compute Trustworthy Robustness Certifications

The paper introduces a novel approach to computing robustness certifications for neural networks, focusing on the apothem measure, which allows for the determination of apothem-optimal certifications with a linear number of calls to a neural network verifier. It highlights the limitations of existing volume-optimal certification methods due to intractability and presents dual certifications that provide tighter bounds. The proposed ParallelepipedoNN system demonstrates at least a two-fold improvement in minimum edge length on the MNIST and Fashion MNIST benchmarks, which is significant for practitioners seeking efficient methods to enhance neural network robustness against adversarial attacks.