The professionalism of a human doctor in outpatient service depends on two core abilities: the ability to make accurate medical decisions and the medical consultation skill to conduct strategic, empathetic patient inquiry. Existing Large Language Models (LLMs) have achieved remarkable accuracy on medical decision-making benchmarks. However, they often lack the ability to conduct the strategic and empathetic consultation, which is essential for real-world clinical scenarios. To address this gap, we propose Doctor-R1, an AI doctor agent trained to master both of the capabilities by ask high-yield questions and conduct strategic multi-turn inquiry to guide decision-making. Our framework introduces three key components: a multi-agent interactive environment, a two-tiered reward architecture that separately optimizes clinical decision-making and communicative inquiry skills, and an experience repository to ground policy learning in high-quality prior trajectories. We evaluate Doctor-R1 on OpenAI's HealthBench and MAQuE, assessed across multi-facet metrics, such as communication quality, user experience, and task accuracy. Remarkably, Doctor-R1 surpasses state-of-the-art open-source specialized LLMs by a substantial margin with higher parameter efficiency and outperforms powerful proprietary models. Furthermore, the human evaluations show a strong preference for Doctor-R1 to generate human-preferred clinical dialogue, demonstrating the effectiveness of the framework.

Abstract: Addressing the core problem of insufficient trustworthiness in industrial fault diagnosis, stemming from the limitations of existing methods -- both traditional and deep learning - based -- in terms of interpretability, generalization, and uncertainty quantification, this paper proposes a trustworthy industrial fault diagnosis architecture, the Hierarchical Cognitive Arbitration Architecture (HCAA), which integrates probabilistic models with Large Language Models (LLMs). The architecture conducts a preliminary analysis via a diagnostic engine based on a Bayesian network and features an LLM - driven cognitive arbitration module with multimodal input capabilities. This module performs expert - level arbitration on the initial diagnosis by analyzing structured features and diagnostic charts, holding the priority to make the final decision upon detecting conflicts. To ensure the reliability of the system's output, the architecture integrates a confidence calibration module based on Temperature Scaling and a risk assessment module, which objectively quantify system trustworthiness using metrics like Expected Calibration Error (ECE). Experimental results on a dataset containing multiple fault types demonstrate that the proposed framework improves diagnostic accuracy by over 28 percentage points compared to baseline models, while the post - calibration ECE is reduced by more than 75%. Case studies confirm that the HCAA effectively corrects misjudgments from traditional models caused by complex feature patterns or knowledge gaps, providing a novel and practical engineering solution for building high - trust, explainable AI diagnostic systems for industrial applications. Keywords: Industrial Fault Diagnosis; Large Language Model (LLM); Hierarchical Cognitive Arbitration; Probabilistic Model; Confidence Calibration; Trustworthy AI 1. Introduction With the deep development of Industry 4.0 and smart manufacturing concepts, modern industrial systems are evolving towards high levels of automation and intelligence. In this process, the reliability and safety of equipment have become key factors determining production efficiency and operational costs. Prognostics and Health Management (PHM), as a core technology, plays an indispensable role in improving equipment reliability, reducing unplanned downtime, and optimizing maintenance costs by monitoring equipment status in real - time, diagnosing potential faults, and predicting remaining useful life [1], [2].

Large language models (LLMs) are increasingly adept at following instructions containing task descriptions to solve complex problems, such as mathematical reasoning and automatic evaluation (LLM-as-a-Judge). However, as prompts grow more complex, models often struggle to adhere to all instructions. This difficulty is especially common when instructive prompts intertwine reasoning directives -- specifying what the model should solve -- with rigid formatting requirements that dictate how the solution must be presented. The entanglement creates competing goals for the model, suggesting that more explicit separation of these two aspects could lead to improved performance. To this front, we introduce Deco-G, a decoding framework that explicitly decouples format adherence from task solving. Deco-G handles format compliance with a separate tractable probabilistic model (TPM), while prompts LLMs with only task instructions. At each decoding step, Deco-G combines next token probabilities from the LLM with the TPM calculated format compliance likelihood to form the output probability. To make this approach both practical and scalable for modern instruction-tuned LLMs, we introduce three key innovations: instruction-aware distillation, a flexible trie-building algorithm, and HMM state pruning for computational efficiency. We demonstrate the effectiveness of Deco-G across a wide range of tasks with diverse format requirements, including mathematical reasoning, LLM-as-a-judge, and event argument extraction. Overall, our approach yields 1.0% to 6.0% relative gain over regular prompting practice with guaranteed format compliance.

We address the challenge of coordinating multiple robots in narrow and confined environments, where congestion and interference often hinder collective task performance. Drawing inspiration from insect colonies, which achieve robust coordination through stigmergy -- modifying and interpreting environmental traces -- we propose a Stigmergic Multi-Agent Deep Reinforcement Learning (S-MADRL) framework that leverages virtual pheromones to model local and social interactions, enabling decentralized emergent coordination without explicit communication. To overcome the convergence and scalability limitations of existing algorithms such as MADQN, MADDPG, and MAPPO, we leverage curriculum learning, which decomposes complex tasks into progressively harder sub-problems. Simulation results show that our framework achieves the most effective coordination of up to eight agents, where robots self-organize into asymmetric workload distributions that reduce congestion and modulate group performance. This emergent behavior, analogous to strategies observed in nature, demonstrates a scalable solution for decentralized multi-agent coordination in crowded environments with communication constraints.

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

Accurate prediction of financial market volatility is critical for risk management, derivatives pricing, and investment strategy. In this study, we propose a multitude of regime-switching methods to improve the prediction of S&P 500 volatility by capturing structural changes in the market across time. We use eleven years of SPX data, from May 1st, 2014 to May 27th, 2025, to compute daily realized volatility (RV) from 5-minute intraday log returns, adjusted for irregular trading days. To enhance forecast accuracy, we engineered features to capture both historical dynamics and forward-looking market sentiment across regimes. The regime-switching methods include a soft Markov switching algorithm to estimate soft-regime probabilities, a distributional spectral clustering method that uses XGBoost to assign clusters at prediction time, and a coefficient-based soft regime algorithm that extracts HAR coefficients from time segments segmented through the Mood test and clusters through Bayesian GMM for soft regime weights, using XGBoost to predict regime probabilities. Models were evaluated across three time periods--before, during, and after the COVID-19 pandemic. The coefficient-based clustering algorithm outperformed all other models, including the baseline autoregressive model, during all time periods. Additionally, each model was evaluated on its recursive forecasting performance for 5- and 10-day horizons during each time period. The findings of this study demonstrate the value of regime-aware modeling frameworks and soft clustering approaches in improving volatility forecasting, especially during periods of heightened uncertainty and structural change.

Discrete diffusion models have recently emerged as strong alternatives to autoregressive language models, matching their performance through large-scale training. However, inference-time control remains relatively underexplored. In this work, we study how to steer generation toward desired rewards without retraining the models. Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement. We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity under reward optimization. PG-DLM constructs a Markov chain over full denoising trajectories and applies a conditional sequential Monte Carlo kernel to resample them. We derive theoretical guarantees for convergence, including asymptotic consistency and variance bounds. Within this framework, we further analyze trade-offs across four key axes for inference-time scaling under fixed budgets: iterations, samples, denoising steps, and reward estimation. Our analysis shows scaling iterations achieves the best reward-perplexity trade-off. Empirically, PG-DLM consistently outperforms prior methods using MDLM and LLaDA-8B as base models across a wide range of compute budgets for reward-guided generation tasks including toxicity and sentiment control as well as linguistic acceptability.

Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to converge when the number of observations $n$ is large. In this paper we introduce a novel and simple non-reversible sampling scheme for Bayesian finite mixture models, which is shown to drastically outperform classical samplers in many scenarios of interest, especially during convergence phase and when components in the mixture have non-negligible overlap. At the theoretical level, we show that the performance of the proposed non-reversible scheme cannot be worse than the standard one, in terms of asymptotic variance, by more than a factor of four; and we provide a scaling limit analysis suggesting that the non-reversible sampler can reduce the convergence time from O$(n^2)$ to O$(n)$. We also discuss why the statistical features of mixture models make them an ideal case for the use of non-reversible discrete samplers.

Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first Bayesian nonparametric framework targeting total robustness that tackles all three challenges in general nonlinear regression. The framework assigns a Dirichlet process prior to the latent co-variate-response distribution and updates it with posterior pseudo-samples of the latent covariates, thereby providing the Dirichlet process posterior with observation-informed latent inputs and yielding estimators that minimise the discrepancy between Dirichlet process realisations and the model-induced joint law. This design allows practitioners to (i) encode prior beliefs, (ii) choose between pseudo-sampling latent covariates or working directly with error-prone observations, and (iii) tune the influence of prior and data. We establish generalisation bounds that tighten whenever the prior or pseudo-sample generator aligns with the underlying data generating process, ensuring robustness without sacrificing consistency. A gradient-based algorithm enables efficient computations; simulations and two real-world studies show lower estimation error and reduced estimation sensitivity to misspecification compared to Bayesian and frequentist competitors. The framework, therefore, offers a practical and interpretable paradigm for trustworthy regression when data and models are jointly imperfect.

We propose new Markov chain Monte Carlo algorithms to sample a uniform distribution on a convex body $K$. Our algorithms are based on the Alternating Sampling Framework/proximal sampler, which uses Gibbs sampling on an augmented distribution and assumes access to the so-called restricted Gaussian oracle (RGO). The key contribution of this work is the efficient implementation of RGO for uniform sampling on $K$ via rejection sampling and access to either a projection oracle or a separation oracle on $K$. In both oracle cases, we establish non-asymptotic complexities to obtain unbiased samples where the accuracy is measured in Rényi divergence or $χ^2$-divergence.