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Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks
Theory paper derives nearly tight Rademacher complexity bounds for sparsely activated one-hidden-layer ReLU networks.
Building on Awasthi et al. (COLT 2024), the authors bound statistical complexity for networks where each input activates at most k of s hidden units. A support-preserving cover and normalized chaining argument remove the explicit dimension factor, with matching lower bounds up to logarithms. They also derive agnostic minimax excess-risk bounds of order min{1, sqrt(s/(km))} for a normalized bounded loss and show bias bounds comparable to WR restore worst-case rates even on domains where sparsity holds globally.
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Microsoft Fixes 114 Windows Flaws in January 2026 Patch, One Actively Exploited
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Cisco plugs serious flaws in Policy Suite, SD-WAN, and Nexus switches
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