Large-N dynamics of the spiked tensor model with random initial conditions

Non-convex multidimensional optimization and the related problem of finding the global minimum in rough landscapes are crucial challenges of modern science. Such problems were extensively studied in the context of the spin-glass systems [1], and found applications in biology [2], finance [3], and data science [4]. Here, we focus on a task motivated by data science and consider the model of the signal recovering from a noisy high-dimensional data tensor - the spiked tensor model (tensor PCA) [5, 6, 7].