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Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization gap, which is the impact of overfitting. Understanding generalization gap…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper takes the…

We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…

We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we…

The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that…

In this paper, we derive upper bounds on generalization errors for deep neural networks with Markov datasets. These bounds are developed based on Koltchinskii and Panchenko's approach for bounding the generalization error of combined…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…

Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…

I consider the generic situation where a finite number of identical test systems in varying (possibly unknown) initial states are subjected independently to the same unknown process. I show how one can infer from the output data alone…

Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…

We propose a novel framework for exploring weak and $L_2$ generalization errors of algorithms through the lens of differential calculus on the space of probability measures. Specifically, we consider the KL-regularized empirical risk…

In this paper we show that the expected generalisation performance of a learning machine is determined by the distribution of risks or equivalently its logarithm -- a quantity we term the risk entropy -- and the fluctuations in a quantity…

For Internet applications like sponsored search, cautions need to be taken when using machine learning to optimize their mechanisms (e.g., auction) since self-interested agents in these applications may change their behaviors (and thus the…

We introduce a temperature into the exponential function and replace the softmax output layer of neural nets by a high temperature generalization. Similarly, the logarithm in the log loss we use for training is replaced by a low temperature…

Minimax optimization has served as the backbone of many machine learning (ML) problems. Although the convergence behavior of optimization algorithms has been extensively studied in the minimax settings, their generalization guarantees in…

Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…

Understanding and accurately following instructions is critical for large language models (LLMs) to be effective across diverse tasks. In this work, we rigorously examine the key factors that enable models to generalize to unseen…