Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural networks and foundation models has now given rise to a new paradigm in statistical modeling, in which Bayesian inference can be amortized through large-scale learned predictors. In amortized inference, substantial computation is invested upfront to train a neural network that can subsequently produce approximate posterior or predictions at negligible marginal cost across a wide range of tasks. At deployment, amortized inference offers substantial computational savings compared with traditional Bayesian procedures, which generally require repeated likelihood evaluations or Monte Carlo simulations for predictions for each new dataset. Despite the growing popularity of amortized inference, its statistical interpretation and its role within Bayesian inference remain poorly understood. This paper presents statistical perspectives on the working principles of several major neural architectures, including feedforward networks, Deep Sets, and Transformers, and examines how these architectures naturally support amortized Bayesian inference. We discuss how these models perform structured approximation and probabilistic reasoning in ways that yield controlled generalization error across a wide range of deployment scenarios, and how these properties can be harnessed for Bayesian computation. Through simulation studies, we evaluate the accuracy, robustness, and uncertainty quantification of amortized inference under varying signal-to-noise ratios and distributional shifts, highlighting both its strengths and its limitations.

Machine Learning algorithms are ubiquitous in key decision-making contexts such as justice, healthcare and finance, which has spawned a great demand for fairness in these procedures. However, the theoretical properties of such models in relation with fairness are still poorly understood, and the intuition behind the relationship between group and individual fairness is still lacking. In this paper, we provide a theoretical framework based on Sheaf Diffusion to leverage tools based on dynamical systems and homology to model fairness. Concretely, the proposed method projects input data into a bias-free space that encodes fairness constrains, resulting in fair solutions. Furthermore, we present a collection of network topologies handling different fairness metrics, leading to a unified method capable of dealing with both individual and group bias. The resulting models have a layer of interpretability in the form of closed-form expressions for their SHAP values, consolidating their place in the responsible Artificial Intelligence landscape. Finally, these intuitions are tested on a simulation study and standard fairness benchmarks, where the proposed methods achieve satisfactory results. More concretely, the paper showcases the performance of the proposed models in terms of accuracy and fairness, studying available trade-offs on the Pareto frontier, checking the effects of changing the different hyper-parameters, and delving into the interpretation of its outputs.

Explainable artificial intelligence (XAI) is concerned with producing explanations indicating the inner workings of models. For a Rashomon set of similarly performing models, explanations provide a way of disambiguating the behavior of individual models, helping select models for deployment. However explanations themselves can vary depending on the explainer used, and need to be evaluated. In the paper "Evaluating Model Explanations without Ground Truth", we proposed three principles of explanation evaluation and a new method "AXE" to evaluate the quality of feature-importance explanations. We go on to illustrate how evaluation metrics that rely on comparing model explanations against ideal ground truth explanations obscure behavioral differences within a Rashomon set. Explanation evaluation aligned with our proposed principles would highlight these differences instead, helping select models from the Rashomon set. The selection of alternate models from the Rashomon set can maintain identical predictions but mislead explainers into generating false explanations, and mislead evaluation methods into considering the false explanations to be of high quality. AXE, our proposed explanation evaluation method, can detect this adversarial fairwashing of explanations with a 100% success rate. Unlike prior explanation evaluation strategies such as those based on model sensitivity or ground truth comparison, AXE can determine when protected attributes are used to make predictions.

In this paper, we extend the Riesz representation framework to causal inference under sample selection, where both treatment assignment and outcome observability are non-random. Formulating the problem in terms of a Riesz representer enables stable estimation and a transparent decomposition of omitted variable bias into three interpretable components: a data-identified scale factor, outcome confounding strength, and selection confounding strength. For estimation, we employ the ForestRiesz estimator, which accounts for selective outcome observability while avoiding the instability associated with direct propensity score inversion. We assess finite-sample performance through a simulation study and show that conventional double machine learning approaches can be highly sensitive to tuning parameters due to their reliance on inverse probability weighting, whereas the ForestRiesz estimator delivers more stable performance by leveraging automatic debiased machine learning. In an empirical application to the gender wage gap in the U.S., we find that our ForestRiesz approach yields larger treatment effect estimates than a standard double machine learning approach, suggesting that ignoring sample selection leads to an underestimation of the gender wage gap. Sensitivity analysis indicates that implausibly strong unobserved confounding would be required to overturn our results. Overall, our approach provides a unified, robust, and computationally attractive framework for causal inference under sample selection.

We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability-flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the flow ODE. For both applications of the Langevin diffusions, we establish convergence guarantees. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks.

Deep double descent is one of the key phenomena underlying the generalization capability of deep learning models. In this study, epoch-wise double descent, which is delayed generalization following overfitting, was empirically investigated by focusing on the evolution of internal structures. Fully connected neural networks of three different sizes were trained on the CIFAR-10 dataset with 30% label noise. By decomposing the loss curves into signal contributions from clean and noisy training data, the epoch-wise evolutions of internal signals were analyzed separately. Three main findings were obtained from this analysis. First, the model achieved strong re-generalization on test data even after perfectly fitting noisy training data during the double descent phase, corresponding to a "benign overfitting" state. Second, noisy data were learned after clean data, and as learning progressed, their corresponding internal activations became increasingly separated in outer layers; this enabled the model to overfit only noisy data. Third, a single, very large activation emerged in the shallow layer across all models; this phenomenon is referred as "outliers," "massive activations," and "super activations" in recent large language models and evolves with re-generalization. These empirical findings directly link the recent key phenomena of "deep double descent," "benign over-fitting," and "large activation", and support the proposal of a novel scenario for understanding deep double descent. Artificial intelligence technologies have undergone remarkable development in recent years, introducing substantial transformation to social structures and influencing various academic fields. Although these models form the core of such technologies, the fundamental principles underlying their high generalization capability when trained on real-world data remain poorly understood. Recent numerical experiments have empirically revealed various intriguing phenomena related to this gap.

This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain consistent. To this end, we propose a new combinatorial structure in directed acyclic graphs called the directed convex hull, which has turned out to be equivalent to their minimum localized Bayesian networks. An efficient polynomial-time algorithm is devised to identify them by determining the unique directed convex hulls containing the variables of interest from the original networks. Experiments demonstrate that the proposed technique has high dimension reduction capability in real networks, and the efficiency of probabilistic inference based on directed convex hulls can be significantly improved compared with traditional methods such as variable elimination and belief propagation algorithms. The code of this study is open at \href{https://github.com/Balance-H/Algorithms}{https://github.com/Balance-H/Algorithms} and the proofs of the results in the main body are postponed to the appendix.

Decentralized online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time-and agent-varying feedback delays. While recent work has addressed this problem (Nguyen et al., 2024), existing algorithms assume prior knowledge of the total delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of O N $\sqrt$ d tot + N $\sqrt$ T (1-$σ$2) 1/4 , where T is the total horizon, d tot denotes the average total delay across agents, N is the number of agents, and 1 -$σ$ 2 is the spectral gap of the network. Our approach builds upon recent advances in D-OCO (Wan et al., 2024a), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive a sharper regret bound of O N $δ$max ln T $α$ , where $α$ is the strong convexity parameter and $δ$ max is the maximum number of missing observations averaged over agents. We also show that our upper bounds for both settings are tight up to logarithmic factors. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

As vehicles grow more software-dependent, repairing them has become harder than ever. A bill in the US House called the Repair Act would ease those restrictions, but it comes with caveats. Every time you get behind the wheel, your car is collecting data about you. Where you go, how fast you're driving, how hard you brake, and even how much you weigh. All of that data is not typically available to the vehicle owner.

NASA Artemis II plans to launch Feb. 6, 2025, sending astronauts Reid Wiseman, Victor Glover, Christina Koch and Jeremy Hansen on the first crewed lunar mission in 50 years.