גבולות תאורטיים לאמינות של רשתות רלו

תקציר מקורי באנגליתarXiv:2602.18674v2 Announce Type: replace Abstract: We present a theoretical study of the robustness of parameterized neural networks to random input perturbations. Specifically, we analyze local robustness by quantifying the probability that a random L_2-perturbation of a given input results in a correct classification. For deep ReLU networks, we derive lower bounds on local robustness by combining tools from high-dimensional geometry, in particular concentration of measure, with a new characterization of the geometric structure induced by their input-output functions. We prove that each convex polyhedral region in the partition of the input space induced by a ReLU network has at most as many faces as there are network units, regardless of the network depth or architecture. This geometric