Paper
Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks
Authors
Saveliy Baturin
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 $ε$ (extending a known result for the quadratic loss); (ii) obtain an asymptotic upper bound on the energy gap $ε$ 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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.17596v1</id>\n <title>Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks</title>\n <updated>2026-02-19T18:20:21Z</updated>\n <link href='https://arxiv.org/abs/2602.17596v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.17596v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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 $ε$ (extending a known result for the quadratic loss); (ii) obtain an asymptotic upper bound on the energy gap $ε$ 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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-02-19T18:20:21Z</published>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Saveliy Baturin</name>\n </author>\n </entry>"
}