A Unified Matrix-Spectral Framework for Stability and Interpretability in Deep Learning

• URL: http://arxiv.org/abs/2602.01136v1
• Date: Sun, 01 Feb 2026 10:18:37 GMT
• Title: A Unified Matrix-Spectral Framework for Stability and Interpretability in Deep Learning
• Authors: Ronald Katende,
• Abstract summary: We develop a unified framework for analyzing stability and interpretability in deep neural networks.<n>We introduce a Global Matrix Stability Index that aggregates spectral information from Jacobians, parameter gradients, Neural Tangent Kernel operators, and loss Hessians into a single stability scale.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a unified matrix-spectral framework for analyzing stability and interpretability in deep neural networks. Representing networks as data-dependent products of linear operators reveals spectral quantities governing sensitivity to input perturbations, label noise, and training dynamics. We introduce a Global Matrix Stability Index that aggregates spectral information from Jacobians, parameter gradients, Neural Tangent Kernel operators, and loss Hessians into a single stability scale controlling forward sensitivity, attribution robustness, and optimization conditioning. We further show that spectral entropy refines classical operator-norm bounds by capturing typical, rather than purely worst-case, sensitivity. These quantities yield computable diagnostics and stability-oriented regularization principles. Synthetic experiments and controlled studies on MNIST, CIFAR-10, and CIFAR-100 confirm that modest spectral regularization substantially improves attribution stability even when global spectral summaries change little. The results establish a precise connection between spectral concentration and analytic stability, providing practical guidance for robustness-aware model design and training.

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