Optimization Induced Equilibrium Networks: An Explicit Optimization Perspective for Understanding Equilibrium Models.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Optimization Theory

Background:

• Deep neural networks (DNNs) present interpretability challenges.
• Equilibrium models, defined by fixed-point equations, are gaining traction in deep learning.
• Existing DNNs lack a unified optimization-induced interpretability framework.

Purpose of the Study:

• To develop a novel class of equilibrium models with inherent optimization interpretability.
• To introduce Optimization Induced Equilibrium Networks (OptEq) as a unified framework.
• To demonstrate the advantages of OptEq over existing implicit models.

Main Methods:

• Decomposing DNNs into unit layers acting as proximal operators of implicit convex functions.
• Deriving an equilibrium model (OptEq) from the unit layer properties.
• Connecting the equilibrium point of OptEq to solutions of explicit convex optimization problems.
• Introducing prior properties by modifying convex problems or merging information into fixed-point iterations.

Main Results:

• OptEq provides a theoretically grounded connection between equilibrium points and convex optimization solutions.
• The framework allows flexible incorporation of prior knowledge into network architectures and training.
• OptEq demonstrates superior performance compared to previous implicit models, even with fewer parameters.

Conclusions:

• OptEq offers a powerful new paradigm for interpretable deep learning models.
• The optimization-induced approach enhances flexibility and performance in equilibrium models.
• This work bridges the gap between deep learning and convex optimization for enhanced interpretability.