When deploying large language models (LLMs) to safety-critical applications, uncertainty quantification (UQ) is of utmost importance to self-assess the reliability of the LLM-based decisions. However, such decisions typically suffer from overconfidence, particularly after parameter-efficient fine-tuning (PEFT) for downstream domain-specific tasks with limited data. Existing methods to alleviate this issue either rely on Laplace approximation based post-hoc framework, which may yield suboptimal calibration depending on the training trajectory, or variational Bayesian training that requires multiple complete forward passes through the entire LLM backbone at inference time for Monte Carlo estimation, posing scalability challenges for deployment. To address these limitations, we build on the Bayesian last layer (BLL) model, where the LLM-based deterministic feature extractor is followed by random last layer parameters for uncertainty reasoning. Since existing low-rank adapters (LoRA) for PEFT have limited expressiveness due to rank collapse, we address this with Polar-decomposed Low-rank Adapter Representation (PoLAR), an orthogonalized parameterization paired with Riemannian optimization to enable more stable and expressive adaptation. Building on this PoLAR-BLL model, we leverage the variational (V) inference framework to put forth a scalable Bayesian fine-tuning approach which jointly seeks the PoLAR parameters and approximate posterior of the last layer parameters via alternating optimization. The resulting PoLAR-VBLL is a flexible framework that nicely integrates architecture-enhanced optimization with scalable Bayesian inference to endow LLMs with well-calibrated UQ. Our empirical results verify the effectiveness of PoLAR-VBLL in terms of generalization and uncertainty estimation on both in-distribution and out-of-distribution data for various common-sense reasoning tasks.

Differentially private $K$-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has emerged as a rapidly growing alternative framework that is particularly well suited to modern applications involving high-dimensional data and complex machine learning models. Its appeal stems from being both distribution-free -- relying mainly on symmetry assumptions such as exchangeability -- and model-agnostic, treating the learning algorithm as a black box. Even under such limited assumptions, conformal prediction provides exact finite-sample guarantees, though these are typically of a marginal nature that requires careful interpretation. This paper explains the core ideas of conformal prediction and reviews selected methods. Rather than offering an exhaustive survey, it aims to provide a clear conceptual entry point and a pedagogical overview of the field.

Aisasetofweightedlinear combinations of the entries ofX, this problem is often referred to as thematrix sensingproblem.

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences.

R2 considered our method requiring a "discretized proxy." First of all, a different, more challenging optimization problem is studied in our work. The variables in the16 barycenter problem we consider include not only the individual transport plan from each source to the barycenter,17 but importantly also the barycenter itself. Wewould33 like to point out that there are three accepted papers at NeurIPS last year inspired by Wasserstein barycenters. These are37 challenging questions that depend on the specific structure of parameterization and the particular recovery method.38

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that generate independent samples from complex molecular distributions, eliminating the cost of sampling rare transition events. However, a sampling problem remains when computing observables that rely on states which are rare in equilibrium, for example folding free energies. Here, we introduce enhanced diffusion sampling, enabling efficient exploration of rare-event regions while preserving unbiased thermodynamic estimators. The key idea is to perform quantitatively accurate steering protocols to generate biased ensembles and subsequently recover equilibrium statistics via exact reweighting. We instantiate our framework in three algorithms: UmbrellaDiff (umbrella sampling with diffusion models), $Δ$G-Diff (free-energy differences via tilted ensembles), and MetaDiff (a batchwise analogue for metadynamics). Across toy systems, protein folding landscapes and folding free energies, our methods achieve fast, accurate, and scalable estimation of equilibrium properties within GPU-minutes to hours per system -- closing the rare-event sampling gap that remained after the advent of diffusion-model equilibrium samplers.

Two key features make correlation clustering quite suitable in real-world applications.