Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model

In three linesTheoretical study demonstrating that neural networks trained with gradient-based methods can achieve optimal computational-statistical tradeoff for Gaussian single-index models. Proposed algorithm (two-layer network) achieves sample complexity Õ(d^{s*/2} ∨ d) matching SQ lower bounds, with extension to k-sparse case via weight perturbation technique.

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