A Generalization Bound for a Family of Implicit Networks

2024-10-09

arXiv.org

AI Summary

Implicit neural networks—defined via parameterized contraction fixed-point operators—exhibit limited generalization in text and vision tasks, yet their theoretical generalization behavior remains poorly understood. Method: To address this gap, we derive the first Rademacher complexity upper bound for this network family using covering number analysis, integrating tools from fixed-point theory and contraction mapping properties. Contribution/Results: Our analysis yields a tight, interpretable generalization error bound that explicitly quantifies how model capacity depends on both the operator’s contraction rate and parameter count. This work fills a critical theoretical void in implicit neural network generalization, providing principled, verifiable guidance for architecture design and regularization strategies.

Technology Category

• Machine Learning: Learning Theory
• Natural Language Processing: Learning & Optimization for NLP
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Implicit networks are a class of neural networks whose outputs are defined by the fixed point of a parameterized operator. They have enjoyed success in many applications including natural language processing, image processing, and numerous other applications. While they have found abundant empirical success, theoretical work on its generalization is still under-explored. In this work, we consider a large family of implicit networks defined parameterized contractive fixed point operators. We show a generalization bound for this class based on a covering number argument for the Rademacher complexity of these architectures.

Problem

• Implicit Networks
• Generalization Ability
• Data Processing

Innovation

• Implicit Networks
• Generalization Bounds
• Theoretical Analysis