Higher-Order Certified Robustness for Regression

Collection of new machine-learning theory papers: (1) "Higher-Order Certified Robustness for Regression" extends randomized smoothing to regression via prediction-centered certificates that incorporate means, variances and gradients, showing gradient-aware certificates tighten robustness (MNIST rotation demos). (2) "Deep Neural Variation Spaces" builds a unified function-space framework for deep fully-connected networks (homogeneous and non-homogeneous activations), proving representer theorems, complexity bounds and a ReLU "depth saturation" result limiting high-frequency expressivity under a