Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model

18 Jul 2019Stefano Sarao MannelliGiulio BiroliChiara CammarotaFlorent KrzakalaLenka Zdeborová

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a quantitative theory explaining this behaviour in a spiked matrix-tensor model... (read more)

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