Counting stationary points of the loss function in the simplest constrained least-square optimization

Abstract

We use Kac-Rice method to analyze statistical features of an "optimization landscape" of the loss function in a random version of the Oblique Procrustes Problem, one of the simplest optimization problems of the least-square type on a sphere.

arXiv commentThe text is based on the presentation at the workshop "Random Matrix Theory: Applications in the Information Era", 29 Apr 2019 -- 3 May 2019 2019, Krakow, Poland

References in corpus (5)

• The Loss Surfaces of Multilayer Networks
• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
• On the number of connected components of random algebraic hypersurfaces
• Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles

Cited by in corpus (4)

• Spherical spin glass model with external field
• Landscape Complexity for the Empirical Risk of Generalized Linear Models
• Superposition of Random Plane Waves in High Spatial Dimensions: Random Matrix Approach to Landscape Complexity
• Optimization landscape in the simplest constrained random least-square problem