2023/04/29 by Joey Huchette, Huchette, Joey, Gonzalo Muñoz +5 · 3 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and Algorithms #Neural Networks and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2305.00241
openalex publication_date 2023/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure of neural networks converged back to simpler representations based on piecewise constant and piecewise linear functions such as the Rectified Linear Unit (ReLU), which became the most commonly used type of activation function in neural networks. That made certain types of network structure \unicodex2014such as the typical fully-connected feedforward neural network\unicodex2014 amenable to analysis through polyhedral theory and to the application of methodologies such as Linear Programming (LP) and Mixed-Integer Linear Programming (MILP) for a variety of purposes. In this paper, we survey the main topics emerging from this fast-paced area of work, which bring a fresh perspective to understanding neural networks in more detail as well as to applying linear optimization techniques to train, verify, and reduce the size of such networks.