Doubt

Ensuring the satisfaction of Signal Temporal Logic (STL) specifications under uncertainty is challenging, as reachability-based monitoring provides guarantees but does not indicate how to restore satisfaction when it becomes indeterminate. A key difficulty is identifying which uncertain components actually affect global satisfaction, especially for nested formulas. This paper introduces a logical dependency tracking framework that propagates uncertainty through the STL structure and captures the causal contribution of reachable sets to satisfaction. By associating markers to uncertain predicates and propagating them via three-valued semantics, we extract in milliseconds a compact Disjunctive Normal Form (DNF) of sufficient constraints, avoiding combinatorial enumeration. As an application, we formulate control correction as a minimum-effort optimization problem. Using zonotopic reachability, the derived constraints are enforced via linear programming, yielding corrections that guarantee STL satisfaction under bounded uncertainty and provide certified probabilistic bounds in the stochastic case. We demonstrate the approach on a nonlinear system with nested STL specifications, showing that dependency tracking enables efficient and formally guaranteed correction. The tracking implementation is available at https://github.com/Antoine-Bst/STL-Three-Valued-Clause-Filtering/.

Clinical prediction models are often developed as if the outcome of interest were cleanly observed for every patient. This assumption fails when treatment decisions make the clinically relevant outcome permanently unobservable. As a case study of this problem, we consider post-cardiac-arrest neurological prognostication using a cohort of 2,497 patients, including 1,429 patients whose outcomes were rendered indeterminate by treatment decisions. These patients with indeterminate outcomes were reviewed by independent clinical experts, who provided their guesses of counterfactual outcomes about what would have happened to the patients. We refer to these patients as uncertain cases. We also have patients for whom we observe their clinically relevant outcomes; we refer to these patients as certain cases. We propose a framework for evaluating prediction models that explicitly splits the evaluation between certain and uncertain cases. Here, we cannot easily evaluate both types of cases in a uniform manner as the available target labels differ. We then propose a simple prediction model that uses target labels from both certain and uncertain cases in a manner that allows us to trade off between them. Across the proposed neural model and a collection of tabular baselines, models with similar certain-case AUROC can nevertheless differ substantially in both certain-case Brier score and their probability estimates for uncertain cases. Improving alignment with target labels of uncertain cases for our proposed model generally comes at the cost of worse accuracy on certain cases, highlighting an explicit tradeoff that standard evaluation conceals. These results show that when treatment decisions determine whether clinically meaningful outcomes remain observable, conventional evaluation metrics can miss important failure modes in the very patients for whom prognostic support matters most.

GK is a query-directed first-order prover that extends ordinary resolution-based proof search with explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions. It works directly with non-ground clauses, including equality and function terms. Candidate proofs are found by bounded first-order proof search; exception conditions of defaults are checked by further bounded searches, recursively when exceptions themselves depend on defaults. This avoids requiring a finite global grounding, while allowing incomplete searches to be reported as such. This paper adds structure-preserving quantitative reporting to that framework. Retained proof histories are used in two calculations. The first reconstructs the uncertain ground premises used by each proof and computes the probability that at least one retained proof is available, without counting shared premises independently. The second resolves positive and negative support at intermediate atoms before that support is propagated through later rules; the same calculation evaluates uncertain exception conditions for individual rule applications. Reports separate positive support, negative support, conflict, and ignorance and identify detected incomplete calculations or fallbacks. The implementation performs bounded reconstruction and dependency traversal after proof search and still requires no global grounding. Analytic examples and independent simulators reproduce the reference calculations on their stated fragments. Comparisons with probabilistic logic, probabilistic ASP, default logic, and goal-directed ASP identify cases of agreement, semantic difference, unsupported translation, and incomplete computation.

Diffusion language models use broad context to create text, suggesting they might handle input noise better than standard models. Testing reveals this is only partially true. Internally, diffusion models detect text errors highly accurately. Externally, their reported certainty ignores this signal. As accuracy drops due to noise, confidence stays near its maximum and the ability to correctly rank answers degrades toward random chance. We call this mismatch the representation confidence gap. The visible concentration of high certainty scores is a misleading surface symptom. Standard math adjustments remove this concentration but fail to fix the underlying loss of ranking order. This ranking deficit favors standard models under noisy conditions and resists common remedies. Matching training recovers accuracy but not ranking, while score recalibration and input level error signals cannot reorder the final answers. However, the information needed to properly evaluate an answer survives in the hidden states. A lightweight extraction tool uses this signal to improve ranking. This approach is highly efficient because it leaves the base model completely frozen and requires zero additional text generation steps. We present this tool to prove the signal exists, while clearly noting its limits. Ultimately, certainty reliability is a more pressing limit than overall accuracy under noisy conditions.

The proliferation of low-altitude intelligent agents is increasing the demand for timely and socially responsible collaborative sensing in dynamic urban environments. However, jointly addressing heterogeneous spatiotemporal demands, environmental uncertainty, and human-centered operational constraints remains challenging. This paper studies 3D multi-UAV path planning and task assignment under uncertain ground PoI demands. Unlike existing work assuming static and fully known PoIs, we model persistent, temporally predictable, and emergent demands within a unified framework. We further incorporate altitude-dependent societal and environmental costs, including noise exposure and public safety risks, to balance sensing performance with socially compliant operations. To solve the resulting large-scale mixed-integer nonlinear problem, we propose FORTUNE, a hierarchical offline-online framework. Offline, a Transformer predicts Type-II PoI activation windows, while an enhanced sparrow search algorithm generates coordinated flight plans through priority-aware decoding and danger-aware evolution. Online, a lightweight refinement module accommodates emerging Type-III PoIs while preserving global mission coherence. Experiments on real-world traffic data and synthetic scenarios show that FORTUNE consistently outperforms state-of-the-art methods in effectiveness, scalability, and practical applicability.

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

The language models that underpin agents have seen a rapid rise in performance on function calling benchmarks. However, the metrics used in the training and evaluation of these models often encourage models to make positive claims even when the answer is uncertain, leading to hallucinations. Such hallucinations can be disastrous when language models are trusted to use function calls to make decisions in high stakes applications. To that end, we propose an agent evaluation metric that takes into account the negative outcomes associated with incorrect function calls. Further, to catch hallucinations before they can cause harm, we propose a lightweight trainable filter that can quantify a language model's uncertainty and remove potentially harmful function calls. By training that filter to detect and suppress uncertain function calls without modifying the underlying model, we demonstrate a practical path toward agents that know when to say "I don't know," a property we argue is essential to production reliability.

Reliable perception in adverse conditions remains challenging for autonomous systems, as cameras and LiDAR degrade in poor lighting or weather. Millimetre-wave FMCW radar is robust to such conditions, but its elevation collapse limits geometric reasoning. We observe that vehicle chassis occlude radar rays and form a distinctive geometric shadow, and its consistency can enable us to infer useful information about objects whose returns intersect this shadow. Motivated by this observation, we propose a method to recover the 3D, in-plane inclination of nearby slender vertical objects from this cue. The object inclination is retrieved without assumptions about the wider scene, but through an analytical, closed-form mapping between its radar return boundaries and the opening angle. Validation in simulation and experimentation on a Navtech CTS350-X radar shows that inclinations can be estimated under practical conditions, with segmentation of the object in the radar scan emerging as the main bottleneck. This work highlights chassis shadows as a novel geometric cue, extending the role of 2D rotating radar beyond localisation and toward 3D scene reconstruction.

Reinforcement Learning (RL) policies often degrade in unfamiliar environments because they lack explicit deliberation. We propose Plan, Align, Commit, Think (PACT), a hybrid architecture that combines a fast, reactive RL policy with a slow, deliberative Small Language Model (SLM) planner. PACT invokes the SLM asynchronously to generate and validate candidate action plans. Once a plan is verified through simulation as safe, feasible, and complete, it is executed directly, bypassing the RL policy without retraining or modifying it. Evaluated on three FrozenLake configurations of increasing difficulty, PACT outperforms all baselines while relying on a 2B-parameter SLM backbone, suggesting that deliberative planning and reactive execution are more powerful in concert than either is alone in these settings.

Evaluating new large language models typically requires costly human annotation campaigns at scale. LLM-as-a-judge offers a cheaper alternative, but judge scores carry systematic errors - such as position bias, self-preference, or intransitivity - that can strongly miscalibrate the resulting rankings. We quantify the resulting judge-human disagreement at two complementary levels. At the local level, we estimate per-battle uncertainty from the judge's own score differences by propagating calibrated win probabilities rather than hard labels into the Bradley-Terry procedure. This alone provides a drastic improvement to Elo estimation accuracy, bringing LLM-derived ratings within 17.9 Elo MAE of human-derived ones when averaged over 55 held-out models on LMArena. At the global level, we apply split conformal prediction to the residual gap between LLM-derived and human-derived Elo ratings across held-out models, producing prediction intervals with distribution-free marginal coverage guarantees that account for irreducible LLM-human disagreement. Together, these two layers yield a low-cost evaluation tool that provides developers with calibrated Elo estimates and honest uncertainty bounds, without access to large-scale human annotations. To facilitate reproducibility, we release our code at https://github.com/kargibora/SoftElo .

Scientific discovery workflows rely heavily on lab notes, where researchers record observations, interpret uncertain results, and plan follow-up experiments. Unlike polished publications, lab notes preserve evolving scientific reasoning, tacit scientific knowledge, and author uncertainty, giving AI agents access to the process of science. However, most prior work on scientific text focuses on papers, protocols, or structured databases, leaving informal laboratory notes underexplored as inputs to AI agents for science. This gap matters because tacit knowledge in lab notes is not written as a clean set of instructions: validated observations, tentative judgments, and possible experimental next steps often appear in the same passage. If these signals are conflated, an AI agent may mistake uncertain scientific judgments for confirmed conclusions or executable actions. To this end, we present Notes2Skills, a two-stage framework for turning lab notebooks into verifiable skills for scientific AI agents while preserving the author's certainty. Across three wet-lab sessions and seven original downstream configurations, Notes2Skills is the only tested configuration that avoids both observed regime-level failures: over-acting on uncertain notes and missing firm directives. We show that certainty preservation is a key missing piece between lab notebooks and reliable agent skills, opening a path toward safer AI co-scientist systems.

When many people highlight the same document, is the crowd a single consensus, or is it internally structured into reader sub-groups that mark different things -- and is that structure a stable property of a reader or of the document? Building on prior work showing an individual's within-document highlighting signal is a whisper while individuality lives in selection, we ask the group-level question on a co-readership platform using a margin-preserving curveball null. Experiment 1: within a document, readers form strong sub-groups -- pairs agree far beyond what shared salience, mark density, and sentence popularity predict (nearest-neighbour agreement z=+6.3, significant in 88% of documents). Under an eight-block region-preserving null, shared engagement with the same coarse regions of the document accounts for about 40% of this excess; the majority survives as finer reader-specific agreement (z=+3.6, 77% significant). So the within-document crowd is, in a descriptive sense, factional. Experiment 2: is that grouping a stable reader trait? Here we are honest about power. The cross-document split-half reproducibility of a pair's agreement is near zero pooled (+0.078 and 0.000 in two separately drawn samples), and a power calibration shows the test is informative only for pairs that co-read many documents. In the only informative high-overlap subset (k>=4), point estimates are positive but small-sample, imprecise across the separately drawn samples, never significant, and attenuate under the region-preserving null. We therefore leave cross-document stability unresolved: the data is consistent with anything from situational grouping to a weak-to-moderate stable reader trait. The crowd is factional within a document; whether its factions follow the reader across documents is, honestly, beyond our reach.

Educational virtual laboratories can make experimental training more scala-ble, adaptive, and accessible, especially when students have limited access to physical laboratory facilities. However, authoring new simulated laboratory procedures remains costly: educators must describe new equipment, define how instruments and materials interact, and specify valid procedural flows that can be executed or assessed inside the virtual environment. Large lan-guage models can assist in this authoring process by generating detailed ex-perimental procedures, but their output should not be treated as directly exe-cutable plans. They may omit necessary actions, arrange steps in the wrong order, or produce instructions that are logically incorrect or incompatible with the laboratory equipment. This paper presents a prototype framework for managing uncertainty in LLM-generated procedural knowledge for virtu-al laboratory planning. The framework aims to reduce procedural uncertainty by using structured domain representations and uncertain LLM-generated state-transition samples to extract candidate procedural rules, transform them into explicit and inspectable constraints, and use them to repair uncertain procedural steps. Although the motivating domain refers to educational vir-tual laboratories, the underlying problem is more general: managing uncer-tain procedural knowledge for action planning in structured interactive envi-ronments. We illustrate the approach in a virtual laboratory domain involving laboratory instruments, containers, tools, and material-transfer actions.

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models are typically learned from data and often degrade in performance under model uncertainty and distributional shifts between training and deployment. Although several works have explored online adaptation to address this issue, many rely on neural network-based updates that introduce significant computational overhead and lack formal safety guarantees, limiting their suitability for real-time and safety-critical robotic applications. In this work, we propose a unified framework for continual adaptive Koopman learning that enables safe and efficient online refinement of learned models during task execution. An autoencoder-based Koopman model is first learned offline and subsequently refined online through a contractive adaptation law, which provides theoretical convergence guarantees under distributional shifts and model uncertainty. To improve data efficiency and accelerate model refinement, the adaptation mechanism is integrated with an active learning strategy that drives the system to collect informative data while accomplishing task objectives. The resulting control problem is formulated as a nonconvex optimization problem incorporating both active learning objectives and safety constraints. We further derive theoretical bounds on model approximation error and show how these bounds can be incorporated within a robust Model Predictive Control (MPC) framework to provide formal safety guarantees. The proposed approach unifies learning, excitation, and safety within a single control framework without sacrificing real-time feasibility. Extensive simulation and experimental studies demonstrate superior performance compared to state-of-the-art baselines.

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

Real-time market prediction services need correct predictions before a decision deadline; a correct prediction delivered late is not usable. TIP-Search studies time-predictable inference scheduling over fixed market predictors under uncertain load. It filters conformal latency-quantile feasible models, dispatches over finite workers, and uses shielded constrained online experts to trade accuracy, queue pressure, and deadline risk. On the optimized deployable pool, TIP-Search reaches 0.994 raw accuracy and 0.991 timely accuracy. On official TLOB FI-2010 h=10, TIP-Search++ raises timely accuracy from 0.156 to 0.239 and deadline satisfaction from 0.391 to 0.962. In matched h10 profiled systems replay, OCO-ACPO reaches 0.303 timely accuracy and 0.951 deadline satisfaction, with paired gains over RAMSIS/SneakPeek/utility-style comparators of $+0.00285$ timely accuracy ($p=0.0118$) and $+0.0146$ deadline satisfaction ($p=1.5{\times}10^{-5}$). SA-OCO-ACPO improves timely/deadline service by 0.188--0.417 over CPO under nonstationary stress. The claim is a systems scheduling result, not a broad LOB classifier leaderboard.

Large Language Models (LLMs) often hallucinate, limiting their reliability in sensitive applications. In black-box settings, several self-consistency-based techniques have been proposed for hallucination detection. We empirically show that these methods perform nearly as well as a supervised (black-box) oracle, leaving limited room for further gains within this paradigm. To address this limitation, we explore cross-model consistency checking between the target model and an additional verifier LLM. With this extra information, we observe improved oracle performance compared to purely self-consistency-based methods. We then propose a budget-friendly, two-stage detection algorithm that calls the verifier model only for a subset of cases. It dynamically switches between self-consistency and cross-consistency based on an uncertainty interval of the self-consistency classifier. We provide a geometric interpretation of consistency-based hallucination detection methods through the lens of kernel mean embeddings, offering deeper theoretical insights. Extensive experiments on QA-style hallucination detection benchmarks show that this approach maintains high detection performance while significantly reducing computational cost.

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers' equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.