For quadratic targets in d dimensions, two-layer quadratic networks achieve lower risk when fully trained than in random features or neural tangent regimes if hidden units < d.
Algorithms and Techniques (APPROX/RANDOM 2014), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2014
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Limitations of Lazy Training of Two-layers Neural Networks
For quadratic targets in d dimensions, two-layer quadratic networks achieve lower risk when fully trained than in random features or neural tangent regimes if hidden units < d.