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Minimal-Norm Univariate Two-Layer ReLU Classification: Exact Solutions and Global Optimality with Skip Connections

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

We study minimal-norm interpolation and $\ell_2$-regularized logistic-loss minimization for binary classification by univariate two-layer ReLU networks. We give complete geometric characterizations of the optimal classifiers in function space, resolving how the solutions depend on whether hidden-layer biases are included in the parameter norm. When biases are unpenalized, the minimal-norm interpolators are exactly the continuous piecewise-affine functions that hug every label switch and have kinks of the appropriate convexity. When biases are penalized, the minimizer is unique in function spac

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