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stat.ML2026
Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness
RóisÃn Luo, James McDermott, Colm O'Riordan
Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations. It plays a pivotal role in deep learning, governing \…
stat.ML2026
A Stochastic--Geometric Theory of Scaling Laws in Grokking
RóisÃn Luo, Christian Gagné, Jonas Ngnawé +2
Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged de…
stat.ML2025
Higher-Order Singular-Value Derivatives of Rectangular Real Matrices
RóisÃn Luo, James McDermott, Colm O'Riordan
We present a theoretical framework for deriving the general -th order Fréchet derivatives of singular values in real rectangular matrices, by leveraging reduced resolvent opera…