1. CQnet: convex-geometric interpretation and constraining neural-network trajectories
- Author
-
Peters, Bas
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,68T07 ,Artificial Intelligence (cs.AI) ,Optimization and Control (math.OC) ,Computer Science - Artificial Intelligence ,I.2.6 ,G.1.6 ,FOS: Mathematics ,Mathematics - Optimization and Control ,Machine Learning (cs.LG) - Abstract
We introduce CQnet, a neural network with origins in the CQ algorithm for solving convex split-feasibility problems and forward-backward splitting. CQnet's trajectories are interpretable as particles that are tracking a changing constraint set via its point-to-set distance function while being elements of another constraint set at every layer. More than just a convex-geometric interpretation, CQnet accommodates learned and deterministic constraints that may be sample or data-specific and are satisfied by every layer and the output. Furthermore, the states in CQnet progress toward another constraint set at every layer. We provide proof of stability/nonexpansiveness with minimal assumptions. The combination of constraint handling and stability put forward CQnet as a candidate for various tasks where prior knowledge exists on the network states or output., 12 pages, 7 figures
- Published
- 2023