CQnet: convex-geometric interpretation and constraining neural-network trajectories

TL;DR

CQnet is a neural network inspired by convex split-feasibility algorithms, offering interpretable trajectories constrained by learned and deterministic sets, with proven stability, suitable for tasks with prior knowledge.

Contribution

Introduces CQnet, a neural network with convex-geometric interpretation, incorporating learned constraints and stability guarantees for improved interpretability and task suitability.

Findings

Trajectory interpretation as particles tracking changing constraints

Incorporates learned and deterministic constraints at each layer

Proven stability and nonexpansiveness under minimal assumptions

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.