Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions

Understand

We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges.

• Such energy landscapes arise in glass physics and inference.
• In particular we focus on random Gaussian functions, and on the spiked-tensor model and generalizations.
• We thoroughly analyze the statistical properties of the corresponding landscapes and characterize the associated geometrical phase transitions.