Isotropic Curvature Model for Understanding Deep Learning Optimization: Is Gradient Orthogonalization Optimal?

arXiv — cs.LGTuesday, November 4, 2025 at 5:00:00 AM
A new model called the isotropic curvature model has been introduced to analyze deep learning optimization. This model focuses on the matrix structure of weights and assumes isotropy of curvature in the loss function. By incorporating second-order Hessian and higher-order terms, it provides a framework for understanding optimization over a single iteration. This is significant as it offers a convex optimization program that can be analyzed, potentially leading to improvements in deep learning techniques.
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