2021/02/23 by Stefano Sarao Mannelli, Mannelli, Stefano Sarao, Pierfrancesco Urbani +1 · 1 citation
Computer Science · Engineering · Mathematics · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2102.11755
openalex publication_date 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss functions, their behaviour in generically non-convex, high dimensional landscapes is poorly understood. In this work, we use dynamical mean field theory techniques to describe analytically the average dynamics of these methods in a prototypical non-convex model: the (spiked) matrix-tensor model. We derive a closed set of equations that describe the behaviour of heavy-ball momentum and Nesterov acceleration in the infinite dimensional limit. By numerical integration of these equations, we observe that these methods speed up the dynamics but do not improve the algorithmic threshold with respect to gradient descent in the spiked model.