Characterizing Learning Dynamics under Relative Reparameterization of Singular Models

Abstract:A common way to analyze learning of statistical models is to consider operations in the models parameter space, however this becomes challenging when there is no one-to-one mapping between the parameter space and the underlying statistical model space. Such ``singular models'' occur frequently and exhibit a characteristic decrease in convergence speed of learning trajectories due to attractor behaviors. In this work, we consider a relative reparameterization technique of the parameter space, which yields a general method for extracting regular sub-models from singular models. On the example of Gaussian Mixture Models and Neural Networks we theoretically and numerically analyze the convergence rate for Gradient Descent under both parameterizations. Analyzing second-order methods and explicit properties of the Fisher Information Matrix we distinguish between differences in convergence behavior arising from algorithmic and intrinsic information-geometric aspects.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2206.08598 [cs.LG]

(or arXiv:2206.08598v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2206.08598 Focus to learn more arXiv-issued DOI via DataCite

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