Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model

Abstract

We provide O(1) asymptotics for the average number of deep minima of the (p,k) spiked tensor model. We also derive an explicit formula for the limiting ground state energy on the N-dimensional sphere, similar to the work of Jagannath-Lopatto-Miolane. Moreover, when the signal to noise ratio is large enough, the expected number of deep minima is asymptotically finite as N tends to infinity and we determine its limit as the signal-to-noise ratio diverges.

arXiv comment24 pages, 2 figures

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Cited by in corpus (1)

• Functional Renormalization for Signal Detection: Dimensional Analysis and Dimensional Phase Transition for Nearly Continuous Spectra Effective Field Theory