רשתות עם וצ' סיומטרי: פרוס וקונטרה

תקציר מקורי באנגליתarXiv:2502.02679v3 Announce Type: replace-cross Abstract: Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of networks on approximation capabilities is compared with its influence on consistency in learning from samples of data. It is shown that, whereas finite VC dimension is desirable for uniform convergence of empirical errors, it may not be desirable for approximation of functions drawn from a probability distribution modeling the likelihood that they occur in a given type of application. Based on the concentration-of-measure properties of high dimensional geometry, it is proven that both errors in app