Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can derive a quantum generalization of the Fisher information matrix in a natural way as the Hessian matrix arising in a Taylor expansion of a smooth divergence. Such an approach is appealing for quantum information theorists, given the ubiquity of divergences in quantum information theory. In contrast to the classical case, there is not a unique quantum generalization of the Fisher information matrix, similar to how there is not a unique quantum generalization of the relative entropy or the Rényi relative entropy. In this paper, I derive information matrices arising from the log-Euclidean, $α$-$z$, and geometric Rényi relative entropies, with the main technical tool for doing so being the method of divided differences for calculating matrix derivatives. Interestingly, for all non-negative values of the Rényi parameter $α$, the log-Euclidean Rényi relative entropy leads to the Kubo-Mori information matrix, and the geometric Rényi relative entropy leads to the right-logarithmic derivative Fisher information matrix. Thus, the resulting information matrices obey the data-processing inequality for all non-negative values of the Rényi parameter $α$ even though the original quantities do not. Additionally, I derive and establish basic properties of $α$-$z$ information matrices resulting from the $α$-$z$ Rényi relative entropies. For parameterized thermal states and time-evolved states, I establish formulas for their $α$-$z$ information matrices and hybrid quantum-classical algorithms for estimating them, with applications in quantum Boltzmann machine learning.

We introduce MedAgentGym, a scalable and interactive training environment designed to enhance coding-based biomedical reasoning capabilities in large language model (LLM) agents. MedAgentGym comprises 72,413 task instances across 129 categories derived from 12 authentic real-world biomedical scenarios. Tasks are encapsulated within executable sandbox environments, each featuring detailed task specifications, interactive feedback mechanisms, verifiable ground truth annotations, and scalable training trajectory generation. Extensive benchmarking of 29 LLMs reveals substantial performance disparities in biomedical data science between commercial and open-source LLMs. Leveraging efficient multi-threaded and multi-turn trajectory sampling in MedAgentGym, Med-Copilot achieves performance gains of +43.02% and +45.28% from offline and online reinforcement learning, respectively, demonstrating MedAgentGym as an effective training ground while establishing itself as a cost-effective, privacy-preserving alternative competitive with proprietary LLMs (gpt-4o). By offering a unified execution environment with a comprehensive benchmark and accessible, extensible training resources, MedAgentGym delivers an integrated platform to develop LLM-based coding assistants for advanced biomedical data science.

Data from such models often exhibits significant deviations from classical Gaussian approximations. A natural class of statistics to analyze in such models are conditionally centered averages (see [30, 63, 52]), where one recenters the observations by their mean, given all other observations. Crucially, such conditionally centered CLTs are closely tied to maximum pseudolikelihood estimators (MPLEs) through the MPLE score (see [64, 60, 41]). This connection is practically important because in many graphical/Markov random field models (such as Ising models, exponential random graph models (ERGMs), etc.), computing the MLE is impeded by an intractable normalizing constant, whereas pseudolikelihood replaces the joint likelihood with a product of tractable conditional models, scales to large networks, and is widely usable in practice. However, most existing theory for conditionally centered statistics and for MPLE focuses on local dependence -- e.g., bounded degree or sparse neighborhoods -- and does not cover realistic dense regimes in which every node may have many connections (which scale with the size of the network). This paper bridges that gap by developing a general limit theory for conditionally centered statistics under weak and verifiable assumptions. Our results accommodate both sparse and dense interactions, as well as regular and irregular network connections. In particular, we deliver valid studentized inference for pseudolikelihood in network/Markov random field settings. As examples, we obtain new CLTs for conditionally centered averages and pseudo-likelihood estimators in Ising models (with pairwise and tensor interactions), and exponential random graph models, without imposing sparsity, regularity, or high temperature restrictions.

6G networks are envisioned to support on-demand AI model downloading to accommodate diverse inference requirements of end users. By proactively caching models at edge nodes, users can retrieve the requested models with low latency for on-device AI inference. However, the substantial size of contemporary AI models poses significant challenges for edge caching under limited storage capacity, as well as for the concurrent delivery of heterogeneous models over wireless channels. To address these challenges, we propose a fine-grained AI model caching and downloading system that exploits parameter reusability, stemming from the common practice of fine-tuning task-specific models from a shared pre-trained model with frozen parameters. This system selectively caches model parameter blocks (PBs) at edge nodes, eliminating redundant storage of reusable parameters across different cached models. Additionally, it incorporates coordinated multipoint (CoMP) broadcasting to simultaneously deliver reusable PBs to multiple users, thereby enhancing downlink spectrum utilization. Under this arrangement, we formulate a model downloading delay minimization problem to jointly optimize PB caching, migration (among edge nodes), and broadcasting beamforming. To tackle this intractable problem, we develop a distributed multi-agent learning framework that enables edge nodes to explicitly learn mutual influence among their actions, thereby facilitating cooperation. Furthermore, a data augmentation approach is proposed to adaptively generate synthetic training samples through a predictive model, boosting sample efficiency and accelerating policy learning. Both theoretical analysis and simulation experiments validate the superior convergence performance of the proposed learning framework.

Large Language Models (LLMs) reasoning abilities are increasingly being applied to classical board and card games, but the dominant approach -- involving prompting for direct move generation -- has significant drawbacks. It relies on the model's implicit fragile pattern-matching capabilities, leading to frequent illegal moves and strategically shallow play. Here we introduce an alternative approach: We use the LLM to translate natural language rules and game trajectories into a formal, executable world model represented as Python code. This generated model -- comprising functions for state transition, legal move enumeration, and termination checks -- serves as a verifiable simulation engine for high-performance planning algorithms like Monte Carlo tree search (MCTS). In addition, we prompt the LLM to generate heuristic value functions (to make MCTS more efficient), and inference functions (to estimate hidden states in imperfect information games). Our method offers three distinct advantages compared to directly using the LLM as a policy: (1) Verifiability: The generated CWM serves as a formal specification of the game's rules, allowing planners to algorithmically enumerate valid actions and avoid illegal moves, contingent on the correctness of the synthesized model; (2) Strategic Depth: We combine LLM semantic understanding with the deep search power of classical planners; and (3) Generalization: We direct the LLM to focus on the meta-task of data-to-code translation, enabling it to adapt to new games more easily. We evaluate our agent on 10 different games, of which 4 are novel and created for this paper. 5 of the games are fully observed (perfect information), and 5 are partially observed (imperfect information). We find that our method outperforms or matches Gemini 2.5 Pro in 9 out of the 10 considered games.

The real world is inherently non-stationary, with ever-changing factors, such as weather conditions and traffic flows, making it challenging for agents to adapt to varying environmental dynamics. Non-Stationary Reinforcement Learning (NSRL) addresses this challenge by training agents to adapt rapidly to sequences of distinct Markov Decision Processes (MDPs). However, existing NSRL approaches often focus on tasks with regularly evolving patterns, leading to limited adaptability in highly dynamic settings. Inspired by the success of Wavelet analysis in time series modeling, specifically its ability to capture signal trends at multiple scales, we propose WISDOM to leverage wavelet-domain predictive task representations to enhance NSRL. WISDOM captures these multi-scale features in evolving MDP sequences by transforming task representation sequences into the wavelet domain, where wavelet coefficients represent both global trends and fine-grained variations of non-stationary changes. In addition to the auto-regressive modeling commonly employed in time series forecasting, we devise a wavelet temporal difference (TD) update operator to enhance tracking and prediction of MDP evolution. We theoretically prove the convergence of this operator and demonstrate policy improvement with wavelet task representations. Experiments on diverse benchmarks show that WISDOM significantly outperforms existing baselines in both sample efficiency and asymptotic performance, demonstrating its remarkable adaptability in complex environments characterized by non-stationary and stochastically evolving tasks.

Despite rapid progress in building conversational AI agents, robustness is still largely untested. Small shifts in user behavior, such as being more impatient, incoherent, or skeptical, can cause sharp drops in agent performance, revealing how brittle current AI agents are. Today's benchmarks fail to capture this fragility: agents may perform well under standard evaluations but degrade spectacularly in more realistic and varied settings. We address this robustness testing gap by introducing TraitBasis, a lightweight, model-agnostic method for systematically stress testing AI agents. TraitBasis learns directions in activation space corresponding to steerable user traits (e.g., impatience or incoherence), which can be controlled, scaled, composed, and applied at inference time without any fine-tuning or extra data. Using TraitBasis, we extend $τ$-Bench to $τ$-Trait, where user behaviors are altered via controlled trait vectors. We observe on average a 2%-30% performance degradation on $τ$-Trait across frontier models, highlighting the lack of robustness of current AI agents to variations in user behavior. Together, these results highlight both the critical role of robustness testing and the promise of TraitBasis as a simple, data-efficient, and compositional tool. By powering simulation-driven stress tests and training loops, TraitBasis opens the door to building AI agents that remain reliable in the unpredictable dynamics of real-world human interactions. We have open-sourced $τ$-Trai across four domains: airline, retail, telecom, and telehealth, so the community can systematically QA their agents under realistic, behaviorally diverse intents and trait scenarios: https://github.com/collinear-ai/tau-trait.

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.

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.