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Zdeborová - Loss landscape and behaviour of algorithms in the spiked matrix-tensor model


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Zdeborová Lenka

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CEREMADE - UMR 7534
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Zdeborová - Loss landscape and behaviour of algorithms in the spiked matrix-tensor model

A key question of current interest is: How are properties of optimization and sampling algorithms influenced by the properties of the loss function in noisy high-dimensional non-convex settings? Answering this question for deep neural networks is a landmark goal of many ongoing works. In this talk I will answer this question in unprecedented detail for the spiked matrix-tensor model. Information theoretic limits, and Kac-Rice analysis of the loss landscapes, will be compared to the analytically studied performance of message passing algorithms, of the Langevin dynamics and of the gradient flow. Several rather non-intuitive results will be unveiled and explained.

 

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