Deep neural networks (DNNs) typically involve a large number of parameters and are trained to achieve zero or near-zero training error. Despite such interpolation, they often exhibit strong generalization performance on unseen data, a phenomenon that has motivated extensive theoretical investigations. Comforting results show that interpolation indeed may not affect the minimax rate of convergence under the squared error loss. In the mean time, DNNs are well known to be highly vulnerable to adversarial perturbations in future inputs. A natural question then arises: Can interpolation also escape from suboptimal performance under a future $X$-attack? In this paper, we investigate the adversarial robustness of interpolating estimators in a framework of nonparametric regression. A finding is that interpolating estimators must be suboptimal even under a subtle future $X$-attack, and achieving perfect fitting can substantially damage their robustness. An interesting phenomenon in the high interpolation regime, which we term the curse of simple size, is also revealed and discussed. Numerical experiments support our theoretical findings.

Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian graphical model, the nonparametric functional additive graphical model, and the conditional functional graphical model. These models rely either on some parametric form of distributions on random functions, or on additive conditional independence, a criterion that is different from probabilistic conditional independence. In this paper we introduce a nonparametric functional graphical model based on functional sufficient dimension reduction. Our method not only relaxes the Gaussian or copula Gaussian assumptions, but also enhances estimation accuracy by avoiding the ``curse of dimensionality''. Moreover, it retains the probabilistic conditional independence as the criterion to determine the absence of edges. By doing simulation study and analysis of the f-MRI dataset, we demonstrate the advantages of our method.

Bayesian optimisation is a sample efficient method for finding a global optimum of expensive black-box objective functions. Historic datasets from related problems can be exploited to help improve performance of Bayesian optimisation by adapting transfer learning methods to various components of the Bayesian optimisation pipeline. In this study we perform an empirical analysis of various ensemble-based transfer learning Bayesian optimisation methods and pipeline components. We expand on previous work in the literature by contributing some specific pipeline components, and three new real-time transfer learning Bayesian optimisation benchmarks. In particular we propose to use a weighting strategy for ensemble surrogate model predictions based on regularised regression with weights constrained to be positive, and a related component for handling the case when transfer learning is not improving Bayesian optimisation performance. We find that in general, two components that help improve transfer learning Bayesian optimisation performance are warm start initialisation and constraining weights used with ensemble surrogate model to be positive.

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as the system size grows have been lacking. A critical concern is that hyperparameter estimation may diverge for larger networks, undermining the model's reliability. Formulating the system's evolution in a measure transport perspective, we propose a theoretical framework for estimating hyperparameters with mean-type observations, which are prevalent in many scientific applications. Our primary contribution is a nonasymptotic bound for the deviation of estimate of hyperparameters in inhomogeneous complex network dynamical systems with respect to network population size, which is established for a general family of optimization algorithms within a fixed observation duration. While we firstly establish a consistency result for systems with independent nodes, our main result extends this guarantee to the more challenging and realistic setting of weakly-dependent nodes. We validate our theoretical findings with numerical experiments on two representative models: a Susceptible-Infected-Susceptible model and a Spiking Neuronal Network model. In both cases, the results confirm that the estimation error decreases as the network population size increases, aligning with our theoretical guarantees. This research proposes the foundational theory to ensure that hierarchical Bayesian methods are statistically consistent for large-scale inhomogeneous systems, filling a gap in this area of theoretical research and justifying their application in practice.

We present BanditLP, a scalable multi-stakeholder contextual bandit framework that unifies neural Thompson Sampling for learning objective-specific outcomes with a large-scale linear program for constrained action selection at serving time. The methodology is application-agnostic, compatible with arbitrary neural architectures, and deployable at web scale, with an LP solver capable of handling billions of variables. Experiments on public benchmarks and synthetic data show consistent gains over strong baselines. We apply this approach in LinkedIn's email marketing system and demonstrate business win, illustrating the value of integrated exploration and constrained optimization in production.

Macroeconomic conditions influence the environments in which health systems operate, yet their value as leading signals of health system capacity has not been systematically evaluated. In this study, we examine whether selected macroeconomic indicators contain predictive information for several capacity-related public health targets, including employment in the health and social assistance workforce, new business applications in the sector, and health care construction spending. Using monthly U.S. time series data, we evaluate multiple forecasting approaches, including neural network models with different optimization strategies, generalized additive models, random forests, and time series models with exogenous macroeconomic indicators, under alternative model fitting designs. Across evaluation settings, we find that macroeconomic indicators provide a consistent and reproducible predictive signal for some public health targets, particularly workforce and infrastructure measures, while other targets exhibit weaker or less stable predictability. Models emphasizing stability and implicit regularization tend to perform more reliably during periods of economic volatility. These findings suggest that macroeconomic indicators may serve as useful upstream signals for digital public health monitoring, while underscoring the need for careful model selection and validation when translating economic trends into health system forecasting tools.

In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic low dimensionality of the support of the target distribution to accelerate sampling. We show that, using a carefully designed choice of the time-discretization scheme and with sufficiently accurate drift estimates, the RF sampler enjoys an iteration complexity of order $O(k/\varepsilon)$ (up to log factors), where $\varepsilon$ is the precision in total variation distance and $k$ is the intrinsic dimension of the target distribution. In addition, we show that the denoising diffusion probabilistic model (DDPM) procedure is equivalent to a stochastic version of RF by establishing a novel connection between these processes and stochastic localization. Building on this connection, we further design a stochastic RF sampler that also adapts to the low-dimensionality of the target distribution under milder requirements on the accuracy of the drift estimates, and also with a specific time schedule. We illustrate with simulations on the synthetic data and text-to-image data experiments the improved performance of the proposed samplers implementing the newly designed time-discretization schedules.

The first generation of LLMs were largely trained on human-generated data. However, the success of LLMs and their increased adoption has had an unexpected consequence of AI-generated content appearing in places where there was previously none. Thus machine learning practitioners should be aware that there is an increased chance that their training data is contaminated by LLM-generated content. Previous work has looked into the value of synthetic (i.e., AI-generated) data, and showed that while naively adding this data to the training mix may lead to model collapse, being more diligent about which data is added, the amount of curation it undergoes, and the specifics of the training process may mitigate that risk, or reverse it, leading to improved performance. These works almost uniquely focus on the LLM setting, trying to improve state of the art performance on a set of benchmarks. In contrast, in this work we take a traditional learning theory view on this problem. We begin by formalizing the setting and developing a framework that captures the invariants of having natural training data contaminated by synthetic additions. Specifically, we see three salient points: Groundtruth. There exists a (potentially small) set of natural data, coming from the true data generation distribution.

The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches in tensor decompositions. In particular, we describe a basis encoding scheme for functions and model neural decompositions as tensor decompositions. The proposed formalism can be applied to represent logical formulas and probability distributions as structured tensor decompositions. This unified treatment identifies tensor network contractions as a fundamental inference class and formulates efficiently scaling reasoning algorithms, originating from probability theory and propositional logic, as contraction message passing schemes. The framework enables the definition and training of hybrid logical and probabilistic models, which we call Hybrid Logic Network. The theoretical concepts are accompanied by the python library tnreason, which enables the implementation and practical use of the proposed architectures.

Reinforcement learning (RL) has achieved remarkable success in real-world decision-making across diverse domains, including gaming, robotics, online advertising, public health, and natural language processing. Despite these advances, a substantial gap remains between RL research and its deployment in many practical settings. Two recurring challenges often underlie this gap. First, many settings offer limited opportunity for the agent to interact extensively with the target environment due to practical constraints. Second, many target environments often undergo substantial changes, requiring redesign and redeployment of RL systems (e.g., advancements in science and technology that change the landscape of healthcare delivery). Addressing these challenges and bridging the gap between basic research and application requires theory and methodology that directly inform the design, implementation, and continual improvement of RL systems in real-world settings. In this paper, we frame the application of RL in practice as a three-component process: (i) online learning and optimization during deployment, (ii) post- or between-deployment offline analyses, and (iii) repeated cycles of deployment and redeployment to continually improve the RL system. We provide a narrative review of recent advances in statistical RL that address these components, including methods for maximizing data utility for between-deployment inference, enhancing sample efficiency for online learning within-deployment, and designing sequences of deployments for continual improvement. We also outline future research directions in statistical RL that are use-inspired -- aiming for impactful application of RL in practice.