On the Stability of Neural Networks in Deep Learning

2025-10-29

AI Summary

Deep neural networks suffer from stability issues, including drastic prediction fluctuations under minor input/parameter perturbations and optimization difficulties induced by sharp loss landscapes. To address these challenges, this paper proposes a unified multi-perspective stability optimization framework. Our method jointly integrates Lipschitz continuity constraints, randomized smoothing, and loss-function curvature regularization. We design a differentiable Lipschitz-constrained layer and an efficient spectral norm computation algorithm, and establish a model robustness certification mechanism grounded in the Lipschitz constant. Experimental results demonstrate that our approach significantly enhances adversarial robustness and generalization performance, alleviates optimization instability, yields smoother loss landscapes, and provides verifiable stability guarantees—thereby bridging theoretical robustness certification with practical training efficacy.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by sharp loss landscapes. This thesis addresses these issues through the unifying perspective of sensitivity analysis, which examines how neural networks respond to perturbations at both the input and parameter levels. We study Lipschitz networks as a principled way to constrain sensitivity to input perturbations, thereby improving generalization, adversarial robustness, and training stability. To complement this architectural approach, we introduce regularization techniques based on the curvature of the loss function, promoting smoother optimization landscapes and reducing sensitivity to parameter variations. Randomized smoothing is also explored as a probabilistic method for enhancing robustness at decision boundaries. By combining these perspectives, we develop a unified framework where Lipschitz continuity, randomized smoothing, and curvature regularization interact to address fundamental challenges in stability. The thesis contributes both theoretical analysis and practical methodologies, including efficient spectral norm computation, novel Lipschitz-constrained layers, and improved certification procedures.

Problem

• Addressing neural network instability to input perturbations
• Improving optimization stability through loss landscape smoothing
• Enhancing adversarial robustness with probabilistic decision boundaries

Innovation

• Lipschitz networks constrain input perturbation sensitivity
• Curvature regularization smoothens loss function optimization
• Randomized smoothing enhances robustness at decision boundaries