Ensuring that deep learning models are well-calibrated in terms of their predictive uncertainty is essential in maintaining their trustworthiness and reliability, yet despite increasing advances in foundation model research, the relationship between such large language models (LLMs) and their calibration remains an open area of research. In this work, we look at a critical gap in the calibration of LLMs within multilingual settings, in an attempt to better understand how the data scarcity can potentially lead to different calibration effects and how commonly used techniques can apply in these settings. Our analysis on two multilingual benchmarks, over 29 and 42 languages respectively, reveals that even in low-resource languages, model confidence can increase significantly after instruction-tuning on high-resource language SFT datasets. However, improvements in accuracy are marginal or non-existent, resulting in mis-calibration, highlighting a critical shortcoming of standard SFT for multilingual languages. Furthermore, we observe that the use of label smoothing to be a reasonable method alleviate this concern, again without any need for low-resource SFT data, maintaining better calibration across all languages. Overall, this highlights the importance of multilingual considerations for both training and tuning LLMs in order to improve their reliability and fairness in downstream use.

Bayesian model selection commonly relies on Laplace approximation or the Bayesian Information Criterion (BIC), which assume that the effective model dimension equals the number of parameters. Singular learning theory replaces this assumption with the real log canonical threshold (RLCT), an effective dimension that can be strictly smaller in overparameterized or rank-deficient models. We study linear-Gaussian rank models and linear subspace (dictionary) models in which the exact marginal likelihood is available in closed form and the RLCT is analytically tractable. In this setting, we show theoretically and empirically that the error of Laplace/BIC grows linearly with (d/2 minus lambda) times log n, where d is the ambient parameter dimension and lambda is the RLCT. An RLCT-aware correction recovers the correct evidence slope and is invariant to overcomplete reparameterizations that represent the same data subspace. Our results provide a concrete finite-sample characterization of Laplace failure in singular models and demonstrate that evidence slopes can be used as a practical estimator of effective dimension in simple linear settings.

Clinical decision-making demands uncertainty quantification that provides both distribution-free coverage guarantees and risk-adaptive precision, requirements that existing methods fail to jointly satisfy. We present a hybrid Bayesian-conformal framework that addresses this fundamental limitation in healthcare predictions. Our approach integrates Bayesian hierarchical random forests with group-aware con-formal calibration, using posterior uncertainties to weight conformity scores while maintaining rigorous coverage validity. Evaluated on 61,538 admissions across 3,793 U.S. hospitals and 4 regions, our method achieves target coverage (94.3% vs 95% target) with adaptive precision: 21% narrower intervals for low-uncertainty cases while appropriately widening for high-risk predictions. Critically, we demonstrate that well-calibrated Bayesian uncertainties alone severely under-cover (14.1%), highlighting the necessity of our hybrid approach. This framework enables risk-stratified clinical protocols, efficient resource planning for high-confidence predictions, and conservative allocation with enhanced oversight for uncertain cases, providing uncertainty-aware decision support across diverse healthcare settings.

Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt to handle structural noise through regularization. In this work, we explicitly capture structural uncertainty by modeling a posterior distribution over signed adjacency matrices, allowing each edge to be positive, negative, or absent. We propose a sparse signed message passing network that is naturally robust to edge noise and heterophily, which can be interpreted from a Bayesian perspective. By combining (i) posterior marginalization over signed graph structures with (ii) sparse signed message aggregation, our approach offers a principled way to handle both edge noise and heterophily. Experimental results demonstrate that our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise. We provide an anonymous repository at: https://anonymous.4open.science/r/SpaM-F2C8

Abstract--Non-stationary parametric bandits have attracted much attention recently. There are three principled ways to deal with non-stationarity, including sliding-window, weighted, and restart strategies. As many non-stationary environments exhibit gradual drifting patterns, the weighted strategy is commonly adopted in real-world applications. However, previous theoretical studies show that its analysis is more involved and the algorithms are either computationally less efficient or statistically subopti-mal. This paper revisits the weighted strategy for non-stationary parametric bandits. In linear bandits (LB), we discover that this undesirable feature is due to an inadequate regret analysis, which results in an overly complex algorithm design. We propose a refined analysis framework, which simplifies the derivation and, importantly, produces a simpler weight-based algorithm that is as efficient as window/restart-based algorithms while retaining the same regret as previous studies. Furthermore, our new framework can be used to improve regret bounds of other parametric bandits, including Generalized Linear Bandits (GLB) and Self-Concordant Bandits (SCB). Moreover, we extend our framework to non-stationary Markov Decision Processes (MDPs) with function approximation, focusing on Linear Mixture MDP and Multinomial Logit (MNL) Mixture MDP . For both classes, we propose algorithms based on the weighted strategy and establish dynamic regret guarantees using our analysis framework. Index T erms--dynamic regret, non-stationary bandits, discounted factor, online MDPs, function approximation. ON-ST A TIONARY parametric bandits model the sequential decision-making problems where the reward distributions of each arm are structured with an unknown time-varying parameter, which have been extensively studied in recent years [1]-[11] due to their significance in many real-world non-stationary online applications such as recommendation systems [12], [13].

This paper develops a practical framework for using observational data to audit the consumer surplus effects of AI-driven decisions, specifically in targeted pricing and algorithmic lending. Traditional approaches first estimate demand functions and then integrate to compute consumer surplus, but these methods can be challenging to implement in practice due to model misspecification in parametric demand forms and the large data requirements and slow convergence of flexible nonparametric or machine learning approaches. Instead, we exploit the randomness inherent in modern algorithmic pricing, arising from the need to balance exploration and exploitation, and introduce an estimator that avoids explicit estimation and numerical integration of the demand function. Each observed purchase outcome at a randomized price is an unbiased estimate of demand and by carefully reweighting purchase outcomes using novel cumulative propensity weights (CPW), we are able to reconstruct the integral. Building on this idea, we introduce a doubly robust variant named the augmented cumulative propensity weighting (ACPW) estimator that only requires one of either the demand model or the historical pricing policy distribution to be correctly specified. Furthermore, this approach facilitates the use of flexible machine learning methods for estimating consumer surplus, since it achieves fast convergence rates by incorporating an estimate of demand, even when the machine learning estimate has slower convergence rates. Neither of these estimators is a standard application of off-policy evaluation techniques as the target estimand, consumer surplus, is unobserved. To address fairness, we extend this framework to an inequality-aware surplus measure, allowing regulators and firms to quantify the profit-equity trade-off. Finally, we validate our methods through comprehensive numerical studies.

Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target relationship. Our approach relies on a local transfer assumption: the covariate space is partitioned into finitely many cells such that, within each cell, the target regression function can be expressed as a low-complexity transformation of the source regression function. This localized structure enables effective transfer where similarity is present while limiting negative transfer elsewhere. We introduce estimators that jointly learn the local transfer functions and the target regression, together with fully data-driven procedures that adapt to unknown partition structure and transfer strength. We establish sharp minimax rates for target regression estimation, showing that local transfer can mitigate the curse of dimensionality by exploiting reduced functional complexity. Our theoretical guarantees take the form of oracle inequalities that decompose excess risk into estimation and approximation terms, ensuring robustness to model misspecification. Numerical experiments illustrate the benefits of the proposed approach.

Conformal prediction guarantees degrade under distribution shift. We study this using COVID-19 as a natural experiment across 8 supply chain tasks. Despite identical severe feature turnover (Jaccard approximately 0), coverage drops vary from 0% to 86.7%, spanning two orders of magnitude. Using SHapley Additive exPlanations (SHAP) analysis, we find catastrophic failures correlate with single-feature dependence (rho = 0.714, p = 0.047). Catastrophic tasks concentrate importance in one feature (4.5x increase), while robust tasks redistribute across many (10-20x). Quarterly retraining restores catastrophic task coverage from 22% to 41% (+19 pp, p = 0.04), but provides no benefit for robust tasks (99.8% coverage). Exploratory analysis of 4 additional tasks with moderate feature stability (Jaccard 0.13-0.86) reveals feature stability, not concentration, determines robustness, suggesting concentration effects apply specifically to severe shifts. We provide a decision framework: monitor SHAP concentration before deployment; retrain quarterly if vulnerable (>40% concentration); skip retraining if robust.

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.