Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However, this procedure is only straightforward when scores are scalar-valued, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT), which provides a principled method for defining vector-ranks and multivariate quantile regions, though typically with only asymptotic coverage guarantees. We restore finite-sample, distribution-free coverage by conformalizing the vector-valued OT quantile region. Here, a candidate's rank is defined via a transport map computed for the calibration scores augmented with that candidate's score. This defines a continuum of OT problems for which we prove that the resulting optimal assignment is piecewise-constant across a fixed polyhedral partition of the score space. This allows us to characterize the entire prediction set tractably, and provides the machinery to address a deeper limitation of prediction sets: that they only indicate which outcomes are plausible, but not their relative likelihood. In one dimension, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct, to our knowledge, the first multivariate CPDs with finite-sample calibration, i.e., they define a valid multivariate distribution where any derived uncertainty region automatically has guaranteed coverage. We present both conservative and exact randomized versions, the latter resulting in a multivariate generalization of the classical Dempster-Hill procedure.

We introduce the first complete formal solution to corrigibility in the off-switch game, with provable guarantees in multi-step, partially observed environments. Our framework consists of five *structurally separate* utility heads -- deference, switch-access preservation, truthfulness, low-impact behavior via a belief-based extension of Attainable Utility Preservation, and bounded task reward -- combined lexicographically by strict weight gaps. Theorem 1 proves exact single-round corrigibility in the partially observable off-switch game; Theorem 3 extends the guarantee to multi-step, self-spawning agents, showing that even if each head is *learned* to mean-squared error $\varepsilon$ and the planner is $\varepsilon$-sub-optimal, the probability of violating *any* safety property is bounded while still ensuring net human benefit. In contrast to Constitutional AI or RLHF/RLAIF, which merge all norms into one learned scalar, our separation makes obedience and impact-limits provably dominate even when incentives conflict. For settings where adversaries can modify the agent, we prove that deciding whether an arbitrary post-hack agent will ever violate corrigibility is undecidable by reduction to the halting problem, then carve out a finite-horizon "decidable island" where safety can be certified in randomized polynomial time and verified with privacy-preserving, constant-round zero-knowledge proofs.

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic constraints. This framework gives rise to a family of forward-backward algorithms, whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.

Recent advances in large language models (LLMs) have greatly improved their reasoning and decision-making abilities when deployed as agents. Richer reasoning, however, often comes at the cost of longer chain of thought (CoT), hampering interaction efficiency in real-world scenarios. Nevertheless, there still lacks systematic definition of LLM agent efficiency, hindering targeted improvements. To this end, we introduce dual-efficiency, comprising (i) step-level efficiency, which minimizes tokens per step, and (ii) trajectory-level efficiency, which minimizes the number of steps to complete a task. Building on this definition, we propose DEPO, a dual-efficiency preference optimization method that jointly rewards succinct responses and fewer action steps. Experiments on WebShop and BabyAI show that DEPO cuts token usage by up to 60.9% and steps by up to 26.9%, while achieving up to a 29.3% improvement in performance. DEPO also generalizes to three out-of-domain math benchmarks and retains its efficiency gains when trained on only 25% of the data. Our project page is at https://opencausalab.github.io/DEPO.

Autonomous exploration of obstacle-rich spaces requires strategies that ensure efficiency while guaranteeing safety against collisions with obstacles. This paper investigates a novel platform-agnostic reinforcement learning framework that integrates a graph neural network-based policy for next-waypoint selection, with a safety filter ensuring safe mobility. Specifically, the neural network is trained using reinforcement learning through the Proximal Policy Optimization (PPO) algorithm to maximize exploration efficiency while minimizing safety filter interventions. Henceforth, when the policy proposes an infeasible action, the safety filter overrides it with the closest feasible alternative, ensuring consistent system behavior. In addition, this paper introduces a reward function shaped by a potential field that accounts for both the agent's proximity to unexplored regions and the expected information gain from reaching them. The proposed framework combines the adaptability of reinforcement learning-based exploration policies with the reliability provided by explicit safety mechanisms. This feature plays a key role in enabling the deployment of learning-based policies on robotic platforms operating in real-world environments. Extensive evaluations in both simulations and experiments performed in a lab environment demonstrate that the approach achieves efficient and safe exploration in cluttered spaces.

Online social media platforms enable influencers to distribute content and quickly capture audience reactions, significantly shaping their promotional strategies and advertising agreements. Understanding how sentiment dynamics and emotional contagion unfold among followers is vital for influencers and marketers, as these processes shape engagement, brand perception, and purchasing behavior. While sentiment analysis tools effectively track sentiment fluctuations, dynamical models explaining their evolution remain limited, often neglecting network structures and interactions both among blogs and between their topic-focused follower groups. In this study, we tracked influential tech-focused Weibo bloggers over six months, quantifying follower sentiment from text-mined feedback. By treating each blogger's audience as a single "macro-agent", we find that sentiment trajectories follow the principle of iterative averaging -- a foundational mechanism in many dynamical models of opinion formation, a theoretical framework at the intersection of social network analysis and dynamical systems theory. The sentiment evolution aligns closely with opinion-dynamics models, particularly modified versions of the classical French-DeGroot model that incorporate delayed perception and distinguish between expressed and private opinions. The inferred influence structures reveal interdependencies among blogs that may arise from homophily, whereby emotionally similar users subscribe to the same blogs and collectively shape the shared sentiment expressed within these communities.

Abstract--Conventional radio frequency (RF) passive components modeling based on machine learning requires extensive electromagnetic (EM) simulations to cover geometric and frequency design spaces, creating computational bottlenecks. In this paper, we introduce an uncertainty-aware Bayesian online learning framework for efficient parametric modeling of RF passive components, which includes: 1) a Bayesian neural network with reconfigurable heads for joint geometric-frequency domain modeling while quantifying uncertainty; 2) an adaptive sampling strategy that simultaneously optimizes training data sampling across geometric parameters and frequency domain using uncertainty guidance. V alidated on three RF passive components, the framework achieves accurate modeling while using only 2.86% EM simulation time compared to traditional ML-based flow, achieving a 35 speedup. Radio frequency integrated circuits (RFICs) form the cornerstone of modern communication systems, enabling critical technologies from 5G/6G networks to Internet-of-Things (IoT) devices [1]. As operational frequencies increase into millimeter-wave and terahertz regimes, traditional lumped-element circuit models become inadequate in mm-wave circuits.

While intelligent tutoring systems (ITSs) can use information from past students to personalize instruction, each new student is unique. Moreover, the education problem is inherently difficult because the learning process is only partially observable. We therefore develop a dynamic, time-series environment to simulate a classroom setting, with student-teacher interventions - including tutoring sessions, lectures, and exams. In particular, we design the simulated environment to allow for varying levels of probing interventions that can gather more information. Then, we develop reinforcement learning ITSs that combine learning the individual state of students while pulling from population information through the use of probing interventions. These interventions can reduce the difficulty of student estimation, but also introduce a cost-benefit decision to find a balance between probing enough to get accurate estimates and probing so often that it becomes disruptive to the student. We compare the efficacy of standard RL algorithms with several greedy rules-based heuristic approaches to find that they provide different solutions, but with similar results. We also highlight the difficulty of the problem with increasing levels of hidden information, and the boost that we get if we allow for probing interventions. We show the flexibility of both heuristic and RL policies with regards to changing student population distributions, finding that both are flexible, but RL policies struggle to help harder classes. Finally, we test different course structures with non-probing policies and we find that our policies are able to boost the performance of quiz and midterm structures more than we can in a finals-only structure, highlighting the benefit of having additional information.

Accurate prediction of project duration and cost remains one of the most challenging aspects of project management, particularly in resource-constrained and interdependent task networks. Traditional analytical techniques such as the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) rely on simplified and often static assumptions regarding task interdependencies and resource performance. This study proposes a novel resource-based predictive framework that integrates network representations of project activities with graph neural networks (GNNs) to capture structural and contextual relationships among tasks, resources, and time-cost dynamics. The model represents the project as a heterogeneous activity-resource graph in which nodes denote activities and resources, and edges encode temporal and resource dependencies. We evaluate multiple learning paradigms, including GraphSAGE and Temporal Graph Networks, on both synthetic and benchmark project datasets. Experimental results show that the proposed GNN framework achieves an average 23 to 31 percent reduction in mean absolute error compared to traditional regression and tree-based methods, while improving the coefficient of determination R2 from approximately 0.78 to 0.91 for large and complex project networks. Furthermore, the learned embeddings provide interpretable insights into resource bottlenecks and critical dependencies, enabling more explainable and adaptive scheduling decisions.

Personal use of this material is permitted. Abstract--Learning from Demonstration (LfD) has shown to provide robots with fundamental motion skills for a variety of domains. V arious branches of LfD research (e.g., learned dynamical systems and movement primitives) can generally be classified into "time-dependent" or "time-independent" systems. Each provides fundamental benefits and drawbacks - time-independent methods cannot learn overlapping trajectories, while time-dependence can result in undesirable behavior under perturbation. This paper introduces Cluster Alignment for Learned Motions (CALM), an LfD framework dependent upon an alignment with a representative "mean" trajectory of demonstrated motions rather than pure time-or state-dependence. We discuss the convergence properties of CALM, introduce an alignment technique able to handle the shifts in alignment possible under perturbation, and utilize demonstration clustering to generate multi-modal behavior . We show how CALM mitigates the drawbacks of time-dependent and time-independent techniques on 2D datasets and implement our system on a 7-DoF robot learning tasks in three domains. S robots are introduced in industry and domestic settings, there is increasing need for robots to learn fundamental motions for given tasks.