Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare--especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.

Privacy concerns have become increasingly critical in modern AI and data science applications, where sensitive information is collected, analyzed, and shared across diverse domains such as healthcare, finance, and mobility. While prior research has focused on protecting privacy in a single data release, many real-world systems operate under sequential or continuous data publishing, where the same or related data are released over time. Such sequential disclosures introduce new vulnerabilities, as temporal correlations across releases may enable adversaries to infer sensitive information that remains hidden in any individual release. In this paper, we investigate whether an attacker can compromise privacy in sequential data releases by exploiting dependencies between consecutive publications, even when each individual release satisfies standard privacy guarantees. To this end, we propose a novel attack model that captures these sequential dependencies by integrating a Hidden Markov Model with a reinforcement learning-based bi-directional inference mechanism. This enables the attacker to leverage both earlier and later observations in the sequence to infer private information. We instantiate our framework in the context of trajectory data, demonstrating how an adversary can recover sensitive locations from sequential mobility datasets. Extensive experiments on Geolife, Porto Taxi, and SynMob datasets show that our model consistently outperforms baseline approaches that treat each release independently. The results reveal a fundamental privacy risk inherent to sequential data publishing, where individually protected releases can collectively leak sensitive information when analyzed temporally. These findings underscore the need for new privacy-preserving frameworks that explicitly model temporal dependencies, such as time-aware differential privacy or sequential data obfuscation strategies.

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology. Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.

We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbfΩ$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbfΩ|^2)$ time while using $\mathcal{O}(n \cdot |\mathbfΩ|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbfΩ|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines.

In many practical sequential decision-making problems, tracking the state of the environment incurs a sensing/communication/computation cost. In these settings, the agent's interaction with its environment includes the additional component of deciding when to sense the state, in a manner that balances the value associated with optimal (state-specific) actions and the cost of sensing. We formulate this as an expected discounted cost Markov Decision Process (MDP), wherein the agent incurs an additional cost for sensing its next state, but has the option to take actions while remaining `blind' to the system state. We pose this problem as a classical discounted cost MDP with an expanded (countably infinite) state space. While computing the optimal policy for this MDP is intractable in general, we derive lower bounds on the optimal value function, which allow us to bound the suboptimality gap of any policy. We also propose a computationally efficient algorithm SPI, based on policy improvement, which in practice performs close to the optimal policy. Finally, we benchmark against the state-of-the-art via a numerical case study.

Real-world language agents must handle complex, multi-step workflows across diverse Apps. For instance, an agent may manage emails by coordinating with calendars and file systems, or monitor a production database to detect anomalies and generate reports following an operating manual. However, existing language agent benchmarks often focus on narrow domains or simplified tasks that lack the diversity, realism, and long-horizon complexity required to evaluate agents' real-world performance. To address this gap, we introduce the Tool Decathlon (dubbed as Toolathlon), a benchmark for language agents offering diverse Apps and tools, realistic environment setup, and reliable execution-based evaluation. Toolathlon spans 32 software applications and 604 tools, ranging from everyday platforms such as Google Calendar and Notion to professional ones like WooCommerce, Kubernetes, and BigQuery. Most of the tools are based on a high-quality set of Model Context Protocol (MCP) servers that we may have revised or implemented ourselves. Unlike prior works, which primarily ensure functional realism but offer limited environment state diversity, we provide realistic initial environment states from real software, such as Canvas courses with dozens of students or real financial spreadsheets. This benchmark includes 108 manually sourced or crafted tasks in total, requiring interacting with multiple Apps over around 20 turns on average to complete. Each task is strictly verifiable through dedicated evaluation scripts. Comprehensive evaluation of SOTA models highlights their significant shortcomings: the best-performing model, Claude-4.5-Sonnet, achieves only a 38.6% success rate with 20.2 tool calling turns on average, while the top open-weights model DeepSeek-V3.2-Exp reaches 20.1%. We expect Toolathlon to drive the development of more capable language agents for real-world, long-horizon task execution.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic uncertainty based on proper scoring rules, with a particular emphasis on kernel scores. The framework unifies several well-known measures and provides a principled recipe for designing new ones whose behavior, such as tail sensitivity, robustness, and out-of-distribution responsiveness, is governed by the choice of kernel. We prove explicit correspondences between kernel-score characteristics and downstream behavior, yielding concrete design guidelines for task-specific measures. Extensive experiments demonstrate that these measures are effective in downstream tasks and reveal clear trade-offs among instantiations, including robustness and out-of-distribution detection performance.

Agentic AI represents a transformative shift in artificial intelligence, but its rapid advancement has led to a fragmented understanding, often conflating modern neural systems with outdated symbolic models -- a practice known as conceptual retrofitting. This survey cuts through this confusion by introducing a novel dual-paradigm framework that categorizes agentic systems into two distinct lineages: the Symbolic/Classical (relying on algorithmic planning and persistent state) and the Neural/Generative (leveraging stochastic generation and prompt-driven orchestration). Through a systematic PRISMA-based review of 90 studies (2018--2025), we provide a comprehensive analysis structured around this framework across three dimensions: (1) the theoretical foundations and architectural principles defining each paradigm; (2) domain-specific implementations in healthcare, finance, and robotics, demonstrating how application constraints dictate paradigm selection; and (3) paradigm-specific ethical and governance challenges, revealing divergent risks and mitigation strategies. Our analysis reveals that the choice of paradigm is strategic: symbolic systems dominate safety-critical domains (e.g., healthcare), while neural systems prevail in adaptive, data-rich environments (e.g., finance). Furthermore, we identify critical research gaps, including a significant deficit in governance models for symbolic systems and a pressing need for hybrid neuro-symbolic architectures. The findings culminate in a strategic roadmap arguing that the future of Agentic AI lies not in the dominance of one paradigm, but in their intentional integration to create systems that are both adaptable and reliable. This work provides the essential conceptual toolkit to guide future research, development, and policy toward robust and trustworthy hybrid intelligent systems.

Robotic manipulation of deformable and fragile objects presents significant challenges, as excessive stress can lead to irreversible damage to the object. While existing solutions rely on accurate object models or specialized sensors and grippers, this adds complexity and often lacks generalization. To address this problem, we present a vision-based reinforcement learning approach that incorporates a stress-penalized reward to discourage damage to the object explicitly. In addition, to bootstrap learning, we incorporate offline demonstrations as well as a designed curriculum progressing from rigid proxies to deformables. We evaluate the proposed method in both simulated and real-world scenarios, showing that the policy learned in simulation can be transferred to the real world in a zero-shot manner, performing tasks such as picking up and pushing tofu. Our results show that the learned policies exhibit a damage-aware, gentle manipulation behavior, demonstrating their effectiveness by decreasing the stress applied to fragile objects by 36.5% while achieving the task goals, compared to vanilla RL policies.