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Brownian Heads for Deep ReLU Representations: Activation Mass and the Cost of Same-Sample Selection

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

Deep representation learning often selects hidden features and fits the final predictor on the same sample, so fixed-feature analysis performed after selection can omit selection cost. We study the conditional empirical Rademacher complexity of deep ReLU representations followed by bounded-norm predictors in additive or Lévy-Brownian RKHSs, termed Brownian heads. For a fixed representation, we derive an exact dual identity and sharp bounds in terms of activation mass, the average norm of the observed hidden vectors. Under same-sample selection, the representation supremum induces a quadratic R

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