The era of proliferation of large language and image generation models begs the question
of what happens if models are trained on the synthesized outputs of other models. The …

In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design.
Exponents for the decay of the excess generalization error of KRR have been reported in …

There is an increasing realization that algorithmic inductive biases are central in preventing
overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized …

We study the generalization capability of nearly-interpolating linear regressors: ${\beta} $'s
whose training error $\tau $ is positive but small, ie, below the noise floor. Under a random …

Empirically, large-scale deep learning models often satisfy a neural scaling law: the test
error of the trained model improves polynomially as the model size and data size grow …

We develop a framework for analyzing the training and learning rate dynamics on a large
class of high-dimensional optimization problems, which we call the high line, trained using …

Motivated by the recent successes of neural networks that have the ability to fit the data
perfectly\emph {and} generalize well, we study the noiseless model in the fundamental least …

This article provides convergence analysis of online stochastic gradient descent algorithms
for functional linear models. Adopting the characterizations of the slope function regularity …

Stochastic gradient descent (SGD) has been shown to generalize well in many deep
learning applications. In practice, one often runs SGD with a geometrically decaying …

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert
space (RKHS) typically requires the target function to be contained in this kernel space. This …