Manifold-based approach for neural network robustness analysis.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Computational Mathematics

Background:

• Understanding the mathematical underpinnings of neural networks is crucial for robust model evaluation.
• Current methods often rely on specific test datasets, limiting applicability.
• There is a need for intrinsic methods to assess neural network robustness.

Purpose of the Study:

• To introduce algorithms for assessing neural network robustness based on manifold curvature estimation.
• To develop methods that utilize only training data, avoiding the need for adversarial or regular test data.
• To propose a robustness measure independent of network architecture and parameters.

Main Methods:

• Proposed a metric for discrete data manifold curvature using weighted angles between subspaces.
• Introduced a robustness measure derived from manifold geometry, independent of model specifics.
• Developed two additional methods leveraging curvature estimation of manifolds formed by gradient vectors.

Main Results:

• Demonstrated the efficacy of manifold geometry-based methods on the CIFAR-10 dataset across various network models.
• Showcased that robustness can be assessed intrinsically using training data properties.
• Validated the proposed curvature estimation techniques for robustness analysis.

Conclusions:

• Manifold curvature estimation offers a powerful, data-intrinsic approach to neural network robustness analysis.
• These methods can contribute to developing neural network models that are both accurate and robust.
• The proposed techniques pave the way for more reliable and trustworthy AI systems.