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[2602.17596] Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks
Summary
This paper explores the loss landscape of one-hidden-layer ReLU networks, demonstrating that overparameterization leads to smoother landscapes and reduced energy gaps between local and global minima.
Why It Matters
Understanding the loss landscape in machine learning models is crucial for improving optimization techniques. This research provides insights into how overparameterization can simplify the training process, potentially leading to better model performance and efficiency.
Key Takeaways
- Overparameterization leads to a smoother loss landscape in ReLU networks.
- Models at the same loss level can be connected with minimal loss increase.
- Wider networks show reduced energy gaps between local and global minima.
- Empirical results support theoretical findings on loss landscape behavior.
- Understanding these dynamics can enhance optimization strategies in machine learning.
Computer Science > Machine Learning arXiv:2602.17596 (cs) [Submitted on 19 Feb 2026] Title:Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks Authors:Saveliy Baturin View a PDF of the paper titled Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks, by Saveliy Baturin View PDF HTML (experimental) Abstract:We study the topology of the loss landscape of one-hidden-layer ReLU networks under overparameterization. On the theory side, we (i) prove that for convex $L$-Lipschitz losses with an $\ell_1$-regularized second layer, every pair of models at the same loss level can be connected by a continuous path within an arbitrarily small loss increase $\epsilon$ (extending a known result for the quadratic loss); (ii) obtain an asymptotic upper bound on the energy gap $\epsilon$ between local and global minima that vanishes as the width $m$ grows, implying that the landscape flattens and sublevel sets become connected in the limit. Empirically, on a synthetic Moons dataset and on the Wisconsin Breast Cancer dataset, we measure pairwise energy gaps via Dynamic String Sampling (DSS) and find that wider networks exhibit smaller gaps; in particular, a permutation test on the maximum gap yields $p_{perm}=0$, indicating a clear reduction in the barrier height. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2602.17596 [cs.LG] (or arXiv:2602.17596v1 [cs.LG] for this version) http...
