5 papers
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
Andrea Montanari, Kangjie Zhou
Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions. Such cost functions can have a multitude of local optima and yet, gra…
Overparametrized linear dimensionality reductions: From projection pursuit to two-layer neural networks
Andrea Montanari, Kangjie Zhou
Given a cloud of data points in , consider all projections onto -dimensional subspaces of and, for each such projection, the empirical distribut…
Lower Bounds for the Convergence of Tensor Power Iteration on Random Overcomplete Models
Yuchen Wu, Kangjie Zhou
Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture…
Learning time-scales in two-layers neural networks
Raphaël Berthier, Andrea Montanari, Kangjie Zhou
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averagi…
Probabilistic Visibility-Aware Trajectory Planning for Target Tracking in Cluttered Environments
Han Gao, Pengying Wu, Yao Su +4
Target tracking has numerous significant civilian and military applications, and maintaining the visibility of the target plays a vital role in ensuring the success of the tracking…