Deep Neural Network Training as Random Effects: An Optimization-Inference Duality

Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in the over-parameterized regime by showing that the prediction induced by continuous-time neural tangent kernel (NTK) gradient flow is exactly equivalent to that from a classical random-effects model. In this framework, training time acts as a variance component, or equivalently an empirical Bayes covariance hyperparameter, governing the allocation of variation from noise to structured signal. This equivalence reveals an optimization-inference duality: the gradient-flow path is both an optimization trajectory and an empirical Bayes random-effects inference path. Conditional on training time, the network output is the posterior mean of the latent signal, and estimating training time by restricted maximum likelihood (REML) turns early stopping into likelihood-based empirical Bayes inference rather than external tuning. This perspective yields a two-stage inferential procedure. First, a variance-component test determines whether DNN training captures statistically significant structure beyond initialization. Second, conditional on training being warranted, REML provides a likelihood-based early stopping rule. The resulting stopping time admits a spectral interpretation in the NTK eigenbasis, where training proceeds until spectral loss decorrelation is achieved. We further establish that REML-guided early stopping achieves asymptotically optimal prediction error for fixed-design in-sample prediction and, under additional random-design regularity conditions, for out-of-sample prediction. This work reframes DNN training as statistical inference and provides a principled foundation for deciding whether and how long to train deep neural networks.

Harnessing Synthetic Data from Generative AI for Statistical Inference

The emergence of generative AI models has dramatically expanded the availability and use of synthetic data across scientific, industrial, and policy domains. While these developments open new possibilities for data analysis, they also raise fundamental statistical questions about when synthetic data can be used in a valid, reliable, and principled manner. This paper reviews the current landscape of synthetic data generation and use from a statistical perspective, with the goal of clarifying the assumptions under which synthetic data can meaningfully support downstream discovery, inference, and prediction. We survey major classes of modern generative models, their intended use cases, and the benefits they offer, while also highlighting their limitations and characteristic failure modes. We additionally examine common pitfalls that arise when synthetic data are treated as surrogates for real observations, including biases from model misspecification, attenuated uncertainty, and difficulties in generalization. Building on these insights, we discuss emerging frameworks for the principled use of synthetic data. We conclude with practical recommendations, open problems, and cautions intended to guide both method developers and applied researchers.

"Rebuilding" Statistics in the Age of AI: A Town Hall Discussion on Culture, Infrastructure, and Training

This article presents the full, original record of the 2024 Joint Statistical Meetings (JSM) town hall, "Statistics in the Age of AI," which convened leading statisticians to discuss how the field is evolving in response to advances in artificial intelligence, foundation models, large-scale empirical modeling, and data-intensive infrastructures. The town hall was structured around open panel discussion and extensive audience Q&A, with the aim of eliciting candid, experience-driven perspectives rather than formal presentations or prepared statements. This document preserves the extended exchanges among panelists and audience members, with minimal editorial intervention, and organizes the conversation around five recurring questions concerning disciplinary culture and practices, data curation and "data work," engagement with modern empirical modeling, training for large-scale AI applications, and partnerships with key AI stakeholders. By providing an archival record of this discussion, the preprint aims to support transparency, community reflection, and ongoing dialogue about the evolving role of statistics in the data- and AI-centric future.

Advancing Real-time Pandemic Forecasting Using Large Language Models: A COVID-19 Case Study

Forecasting the short-term spread of an ongoing disease outbreak is a formidable challenge due to the complexity of contributing factors, some of which can be characterized through interlinked, multi-modality variables such as epidemiological time series data, viral biology, population demographics, and the intersection of public policy and human behavior. Existing forecasting model frameworks struggle with the multifaceted nature of relevant data and robust results translation, which hinders their performances and the provision of actionable insights for public health decision-makers. Our work introduces PandemicLLM, a novel framework with multi-modal Large Language Models (LLMs) that reformulates real-time forecasting of disease spread as a text reasoning problem, with the ability to incorporate real-time, complex, non-numerical information that previously unattainable in traditional forecasting models. This approach, through a unique AI-human cooperative prompt design and time series representation learning, encodes multi-modal data for LLMs. The model is applied to the COVID-19 pandemic, and trained to utilize textual public health policies, genomic surveillance, spatial, and epidemiological time series data, and is subsequently tested across all 50 states of the U.S. Empirically, PandemicLLM is shown to be a high-performing pandemic forecasting framework that effectively captures the impact of emerging variants and can provide timely and accurate predictions. The proposed PandemicLLM opens avenues for incorporating various pandemic-related data in heterogeneous formats and exhibits performance benefits over existing models. This study illuminates the potential of adapting LLMs and representation learning to enhance pandemic forecasting, illustrating how AI innovations can strengthen pandemic responses and crisis management in the future.