Experimental stability analysis of neural networks in classification problems with confidence sets for persistence diagrams

We investigate classification performance of neural networks (NNs) based on topological insight in an attempt to guarantee stability their inference. NNs which can accurately classify a dataset map it into hidden space while disentangling intertwined data. sometimes acquire forcible mapping disentangle the data, and this generates outliers. The around outliers is unstable because outputs change drastically. Hence, we define stable mean that they do not generate To possibility existence outliers, use persistent homology method estimate confidence set for persistence diagrams. combined enables us test whether focused geometry topologically simple, is, no In work, MNIST CIFAR-10 datasets relationship between characteristics with several NNs. Investigation results show accuracy all superior, exceeding 98%, even though transformed simple. Results also shown by accurate convolutional Therefore, conclude presented investigation necessary NNs, particular deep classification.