Some Results on Neural Network Stability, Consistency, and Convergence: Insights into Non-IID Data, High-Dimensional Settings, and Physics-Informed Neural Networks
Ronald Katende, Henry Kasumba, Godwin Kakuba, John M. Mango
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引用次数: 0
Abstract
This paper addresses critical challenges in machine learning, particularly
the stability, consistency, and convergence of neural networks under non-IID
data, distribution shifts, and high-dimensional settings. We provide new
theoretical results on uniform stability for neural networks with dynamic
learning rates in non-convex settings. Further, we establish consistency bounds
for federated learning models in non-Euclidean spaces, accounting for
distribution shifts and curvature effects. For Physics-Informed Neural Networks
(PINNs), we derive stability, consistency, and convergence guarantees for
solving Partial Differential Equations (PDEs) in noisy environments. These
results fill significant gaps in understanding model behavior in complex,
non-ideal conditions, paving the way for more robust and reliable machine
learning applications.