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

arXiv:2609.28438 · cs.LG · Submitted 2026-09-23 · Read on arXiv

cs.LG

Submitted: 2026-09-23

Updated: 2026-09-23

Code: https://github.com/englert-m/min-norm-univariate-classification

Terminology

• Regularization — 33× in this paper · explained in 3 episodes
• Sparsity — 13× in this paper · explained in 4 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Homogeneity — 5× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Alignment — 3× in this paper · explained in 1 episode
• Benchmark — 3× in this paper · explained in 2 episodes
• Gradient Flow — 3× in this paper · explained in 2 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Generative AI — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Algorithmic Stability — 1× in this paper · explained in 1 episode
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Penalising the biases in norm regularisation enforces sparsity
• Ridgeless Interpolation with Shallow ReLU Networks in $1D$ is Nearest Neighbor Curvature Extrapolation and Provably Generalizes on Lipschitz Functions
• Sufficient Conditions for Stability of Minimum-Norm Interpolating Deep ReLU Networks

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