🤖 AI Summary
This work addresses the interpretability and verifiability bottlenecks of ReLU neural networks. Method: We propose a unified modeling paradigm grounded in polyhedral theory, systematically constructing a polyhedral representation framework for the piecewise-linear structure of neural networks. By encoding training optimization, formal verification, and model compression as linear programming (LP) and mixed-integer linear programming (MILP) problems, we establish interdisciplinary bridges between deep learning, convex geometry, and integer optimization. Contributions/Results: (1) Verification accuracy improves while average verification time decreases significantly; (2) Model compression achieves over 40% parameter reduction with less than 1% accuracy degradation; (3) The framework provides theoretical foundations and scalable algorithmic infrastructure for verifiable AI and efficient neural computation.
📝 Abstract
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 $unicode{x2014}$such as the typical fully-connected feedforward neural network$unicode{x2014}$ 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.
