Accurate uncertainty quantification remains a key challenge for standard LLMs, prompting the adoption of Bayesian and ensemble-based methods. However, such methods typically necessitate computationally expensive sampling, involving multiple forward passes to effectively estimate predictive uncertainty. In this paper, we introduce a novel approach enabling efficient and effective uncertainty estimation in LLMs without sacrificing performance. Specifically, we distill uncertainty-aware teacher models - originally requiring multiple forward passes - into compact student models sharing the same architecture but fine-tuned using Low-Rank Adaptation (LoRA). We compare two distinct distillation strategies: one in which the student employs traditional softmax-based outputs, and another in which the student leverages Dirichlet-distributed outputs to explicitly model epistemic uncertainty via evidential learning. Empirical evaluations on classification datasets demonstrate that such students can achieve comparable or superior predictive and uncertainty quantification performance relative to their teacher models, while critically requiring only a single forward pass. To our knowledge, this is the first demonstration that immediate and robust uncertainty quantification can be achieved in LLMs through evidential distillation.

Given a multivariate function taking deterministic and unc ertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs f or which the probability that the output belongs to a specific region remains below a given threshold. To solve this problem in the context of expensive-to-evaluate black-box functions, we propose a Bayesian active learning strategy based on Gaussian process modeling. The strategy is driven by a nov el sampling criterion, which belongs to a broader principle that we refer to as Expected Estimator Modification (EEM). More specifically, the strategy relies on a novel sampling criterion combined w ith a sequential Monte Carlo framework that enables the construction of batch-sequential designs for the efficient estimation of small quantile sets. The performance of the strategy is illustrated on seve ral synthetic examples and an industrial application case involving the ROTOR37 compressor model.

We introduce the microclustering Ewens--Pitman model for random partitions, obtained by scaling the strength parameter of the Ewens--Pitman model linearly with the sample size. The resulting random partition is shown to have the microclustering property, namely: the size of the largest cluster grows sub-linearly with the sample size, while the number of clusters grows linearly. By leveraging the interplay between the Ewens--Pitman random partition with the Pitman--Yor process, we develop efficient variational inference schemes for posterior computation in entity resolution. Our approach achieves a speed-up of three orders of magnitude over existing Bayesian methods for entity resolution, while maintaining competitive empirical performance.

Cooperative multi-agent reinforcement learning (MARL) is typically formalised as a Decentralised Partially Observable Markov Decision Process (Dec-POMDP), where agents must reason about the environment and other agents' behaviour. In practice, current model-free MARL algorithms use simple recurrent function approximators to address the challenge of reasoning about others using partial information. In this position paper, we argue that the empirical success of these methods is not due to effective Markov signal recovery, but rather to learning simple conventions that bypass environment observations and memory. Through a targeted case study, we show that co-adapting agents can learn brittle conventions, which then fail when partnered with non-adaptive agents. Crucially, the same models can learn grounded policies when the task design necessitates it, revealing that the issue is not a fundamental limitation of the learning models but a failure of the benchmark design. Our analysis also suggests that modern MARL environments may not adequately test the core assumptions of Dec-POMDPs. We therefore advocate for new cooperative environments built upon two core principles: (1) behaviours grounded in observations and (2) memory-based reasoning about other agents, ensuring success requires genuine skill rather than fragile, co-adapted agreements.

Due to practical constraints such as partial observability and limited communication, Centralized Training with Decentralized Execution (CTDE) has become the dominant paradigm in cooperative Multi-Agent Reinforcement Learning (MARL). However, existing CTDE methods often underutilize centralized training or lack theoretical guarantees. We propose Multi-Agent Guided Policy Optimization (MAGPO), a novel framework that better leverages centralized training by integrating centralized guidance with decentralized execution. MAGPO uses an auto-regressive joint policy for scalable, coordinated exploration and explicitly aligns it with decentralized policies to ensure deployability under partial observability. We provide theoretical guarantees of monotonic policy improvement and empirically evaluate MAGPO on 43 tasks across 6 diverse environments. Results show that MAGPO consistently outperforms strong CTDE baselines and matches or surpasses fully centralized approaches, offering a principled and practical solution for decentralized multi-agent learning. Our code and experimental data can be found in https://github.com/liyheng/MAGPO.

Do larger and more capable language models learn to update their "beliefs" about propositions more consistently with Bayes' theorem when presented with evidence in-context? To test this, we formulate a Bayesian Coherence Coefficient (BCC) metric and generate a dataset with which to measure the BCC. We measure BCC for multiple pre-trained-only language models across five model families, comparing against the number of model parameters, the amount of training data, and model scores on common benchmarks. Our results provide evidence for our hypothesis that larger and more capable pre-trained language models assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.

The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their parts. However, there are settings such as mean estimation where we have strong lower bounds, showing that when the two data sources have the same distribution, there is no complementary value to combining the two data sources. In this work we extend the known lower bounds for public-private learning to setting where the two data sources exhibit significant distribution shift. Our results apply to both Gaussian mean estimation where the two distributions have different means, and to Gaussian linear regression where the two distributions exhibit parameter shift. We find that when the shift is small (relative to the desired accuracy), either public or private data must be sufficiently abundant to estimate the private parameter. Conversely, when the shift is large, public data provides no benefit.

Age-specific fertility rates (ASFRs) provide the most extensive record of reproductive change, but their aggregate nature obscures the individual-level behavioral mechanisms that drive fertility trends. To bridge this micro-macro divide, we introduce a likelihood-free Bayesian framework that couples a demographically interpretable, individual-level simulation model of the reproductive process with Sequential Neural Posterior Estimation (SNPE). We show that this framework successfully recovers core behavioral parameters governing contemporary fertility, including preferences for family size, reproductive timing, and contraceptive failure, using only ASFRs. The framework's effectiveness is validated on cohorts from four countries with diverse fertility regimes. Most compellingly, the model, estimated solely on aggregate data, successfully predicts out-of-sample distributions of individual-level outcomes, including age at first sex, desired family size, and birth intervals. Because our framework yields complete synthetic life histories, it significantly reduces the data requirements for building microsimulation models and enables behaviorally explicit demographic forecasts.

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks. Recent advances demonstrate that inference on sparse Bayesian networks can be accelerated using quantum rejection sampling combined with amplitude amplification, leading to a computational speedup in estimating acceptance probabilities.\\ Building on this result, we introduce Quantum Bayesian Reinforcement Learning (QBRL), a hybrid quantum-classical look-ahead algorithm for model-based RL in partially observable environments. We present a rigorous, oracle-free time complexity analysis under fault-tolerant assumptions for the quantum device. Unlike standard treatments that assume a black-box oracle, we explicitly specify the inference process, allowing our bounds to more accurately reflect the true computational cost. We show that, for environments whose dynamics form a sparse Bayesian network, horizon-based near-optimal planning can be achieved sub-quadratically faster through quantum-enhanced belief updates. Furthermore, we present numerical experiments benchmarking QBRL against its classical counterpart on simple yet illustrative decision-making tasks. Our results offer a detailed analysis of how the quantum computational advantage translates into decision-making performance, highlighting that the magnitude of the advantage can vary significantly across different deployment settings.

Adversarial attacks in 3D environments have emerged as a critical threat to the reliability of visual perception systems, particularly in safety-sensitive applications such as identity verification and autonomous driving. These attacks employ adversarial patches and 3D objects to manipulate deep neural network (DNN) predictions by exploiting vulnerabilities within complex scenes. Existing defense mechanisms, such as adversarial training and purification, primarily employ passive strategies to enhance robustness. However, these approaches often rely on pre-defined assumptions about adversarial tactics, limiting their adaptability in dynamic 3D settings. To address these challenges, we introduce Reinforced Embodied Active Defense (Rein-EAD), a proactive defense framework that leverages adaptive exploration and interaction with the environment to improve perception robustness in 3D adversarial contexts. By implementing a multi-step objective that balances immediate prediction accuracy with predictive entropy minimization, Rein-EAD optimizes defense strategies over a multi-step horizon. Additionally, Rein-EAD involves an uncertainty-oriented reward-shaping mechanism that facilitates efficient policy updates, thereby reducing computational overhead and supporting real-world applicability without the need for differentiable environments. Comprehensive experiments validate the effectiveness of Rein-EAD, demonstrating a substantial reduction in attack success rates while preserving standard accuracy across diverse tasks. Notably, Rein-EAD exhibits robust generalization to unseen and adaptive attacks, making it suitable for real-world complex tasks, including 3D object classification, face recognition and autonomous driving.