Abstract
It is important to understand the mathematical foundations of neural networks and to include robustness in model evaluation. Here, we introduce algorithms based on manifold curvature estimation to assess neural network robustness. These algorithms rely solely on training data and do not require regular or adversarial test data. Initially, a metric is proposed to measure the curvature of discrete data manifolds by introducing weighted angles concept between subspaces. Following this, a robustness measure is introduced that is independent of network architecture or model parameters. Lastly, two additional methods are introduced, utilizing curvature estimation of special manifolds formed by using gradient vectors between output and input network layers, alongside manifold curvature estimation. A comprehensive evaluation is provided on multiple network models using the CIFAR-10 dataset. Manifold geometry-based robustness analysis may lead to the development of not only accurate but also robust neural network models.