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Gradient flow on extensive-rank positive semi-definite matrix denoising
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime.
Gradient flow in the gaussian covariate model: exact solution of learning curves and multiple descent structures
Even the least-squares regression has shown atypical features such as the model-wise double descent, and further works have observed triple or multiple descents.
Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature model
A recent line of research has highlighted that random matrix tools can be used to obtain precise analytical asymptotics of the generalization (and training) errors of the random feature model.
Rank-one matrix estimation: analytic time evolution of gradient descent dynamics
Explicit formulas for the whole time evolution of the overlap between the estimator and unknown vector, as well as the cost, are rigorously derived.
