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Under mild assumptions, we investigate the geometry of the loss landscape fortwo-layer neural networks in the vicinity of global minima. Utilizing noveltechniques, we demonstrate: (i) how global minima with zero generalizationerror become geometrically separated from other global minima as the samplesize grows; and (ii) the local convergence properties and rate of gradient flowdynamics. Our results indicate that two-layer neural networks can be locallyrecovered in the regime of overparameterization.

Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization