Uncertainty-Aware Inference

Source term estimation (STE), which aims to estimate key properties of the gas source, is essential for identifying hazardous gas releases. Information-theoretic approaches have been adopted for autonomous STE using mobile sensors due to robustness in noisy environments, yet their online action selection incurs substantial computational cost. Deep reinforcement learning (DRL) provides a promising alternative with its fast decision-making capability. In DRL-based STE, the agent selects actions based on belief states of the source term updated from noisy measurement sequences. However, existing methods rely on random exploration or solely on belief uncertainty reduction without an effective exploration strategy in DRL, which can limit policy robustness in noisy environments. To address this, we propose a curiosity-driven information-guided reinforcement learning for robust and efficient STE. The proposed method promotes active exploration of novel belief state transitions that have not been sufficiently explored during training. We further introduce an uncertainty-adaptive active perception reward to guide efficient source search under uncertainty. Simulations under high-noise conditions and real-world experiments demonstrate the robustness and feasibility of the proposed framework, highlighting its potential for practical STE problems.

Broad Learning System (BLS) offers an efficient alternative to deep architectures by enabling fast learning through randomized feature mapping and closed-form solutions. However, its reliance on squared error loss makes it highly sensitive to noise, outliers, and corrupted labels, limiting its reliability in real-world scenarios. To address this limitation, we propose Wave-BLS, a robust broad learning framework that integrates the wave loss function, which is asymmetric, bounded, and smooth, enabling controlled penalization of large errors. The proposed formulation replaces the standard least-squares objective with a wave-loss-based optimization problem, solved efficiently using a Nesterov accelerated gradient (NAG)-based scheme without requiring matrix inversion, thereby improving scalability. Extensive experiments on 30 UCI benchmark datasets demonstrate that Wave-BLS consistently outperforms classical BLS and several robust variants. Statistical validation using Friedman and Nemenyi post-hoc tests confirms the significance of the observed improvements. Furthermore, robustness evaluations under controlled noise and outlier injection reveal that Wave-BLS exhibits substantially slower performance degradation compared to BLS, even in challenging contamination settings. These results establish Wave-BLS as a stable and robust alternative to existing broad learning models for learning under data uncertainty.

Scientific discovery often involves optimising expensive-to-evaluate objectives over vast, structured, and open-ended hypothesis spaces, such as molecules, protein sequences, and computer programs. Generative models such as large language models (LLMs) provide expressive priors over such spaces, but their likelihoods and self-assessments are unreliable proxies for the objectives and calibrated epistemic uncertainty, especially for novel candidates outside the observed data distribution. We introduce the Large Discovery Model (LDM), an empirically grounded recurrent architecture that couples a generative model with a Bayesian non-parametric reward surrogate model. The generative model proposes and refines candidate designs, while the surrogate predicts their performance and quantifies uncertainty, yielding an uncertainty-aware value that guides candidate generation, refinement, and selection. The discovery memory and the surrogate model are continually updated as each new experimental observation arrives. We evaluate LDM on three scenarios spanning different design modalities and objectives, including neural-network training, antibody design, and molecular optimisation. Compared to LLM-only reflection or traditional statistical search across these domains, LDM achieves a $2.4\times$ greater reduction in validation BPB, an $18.2\%$ relative decrease in binding energy, and more than $60\%$ relative gains in molecular multi-objective performance. These results suggests that LDM could serve as a general-purpose discovery engine for effective search over open-ended hypothesis spaces.

Large language models can extract richer signals from financial news than fixed sentiment lexicons, and recent work has explored feeding such signals into portfolio construction. We study an uncertainty-aware construction that feeds model-predicted risk -- decomposed into aleatoric and epistemic components -- directly into the covariance matrix of portfolio allocators, rather than treating portfolio risk as fixed or adjusting only expected returns. We evaluate the pipeline on Russell 2000 equities under three stock-selection regimes: a pure-alpha trigger that isolates abnormal stock moves not explained by macro indicators, a pure-beta trigger that captures macro-indicator moves before the stock itself fires, and a beta trigger in which both channels agree. Across the full holding-period grid, the separated pure-alpha and pure-beta legs usually dominate the beta intersection on Sharpe and return. Two horizons are especially informative. At one day, pure beta can work under low and moderate transaction costs because it captures immediate lead-lag spillovers from liquid macro and sector indicators into exposed small-cap stocks, but this advantage disappears at 100 bps when turnover and microstructure noise dominate. At 40 days, pure beta works for a different reason: slower macro repricing overtakes the firm-specific pure-alpha channel. The strongest conservative row is pure beta with GPT-4o mini sentiment, a Student-t target, a 40-day holding period, and risk parity allocation, reaching Sharpe 2.33 at 100 bps. The results suggest that stock-selection regime and allocator choice matter at least as much as the sentiment model, and that separating firm-specific and macro-exposure triggers is more informative than requiring both to fire simultaneously.

Quantitative T2* maps have strong potential for biomarker discovery but are limited by long scan times, rendering them impractical in clinical settings. Significant acceleration can be achieved through undersampling in k-space combined with learning-based reconstruction. However, reconstruction artifacts and noise can propagate into downstream T2* fitting, degrading its accuracy. We introduce CUPA-T2*, a framework that explicitly propagates voxel-wise inter-echo uncertainty from stochastic Monte Carlo dropout reconstructions to downstream T2* fitting via covariance-aware sampling. T2* fitting is performed with a heteroscedastic MLP and a correlation-based regularizer that encourages alignment between predicted variance and reconstruction uncertainty. Experiments on accelerated brain MRI data show tissue-dependent behavior: CUPA-T2* achieves competitive overall T2* fitting performance and improves white-matter performance at higher accelerations. Compared with a heteroscedastic baseline, the proposed framework substantially increases alignment between reconstruction uncertainty and predicted T2* variance, while also revealing a trade-off with calibration (ECE) and selective prediction performance (AURC). CUPA-T2* enables reconstruction uncertainty-aware T2* fitting and delivers voxel-wise uncertainty maps to support the interpretation of quantitative T2* estimates.

Concept Bottleneck Models (CBMs) provide an interpretable framework by grounding predictions in human-understandable concepts, enabling semantic inspection and test-time intervention. Recent variants have improved CBMs through richer concept representations, uncertainty estimation, and dependency modeling. However, robust reasoning under unreliable concept states remains underexplored. Without such reasoning, misleading semantic evidence can propagate through the bottleneck, compromising both explanations and downstream predictions. To address this issue, we propose ReCBM, an uncertainty-gated relational reasoning framework for CBMs. ReCBM introduces semantically defined concept relations into the bottleneck and uses uncertainty to guide their refinement. By modeling co-occurrence, implication, and exclusion, ReCBM specifies how evidence is exchanged across concepts, while uncertainty modulates the contribution of each concept during this process. Experiments across diverse datasets showed that ReCBM improved concept and task recovery under missing and flipped concepts, supported uncertainty-aware intervention, and extracted compact task-relevant concept subsets without degrading downstream performance.

Automatic RF modulation recognition is of critical importance in spectrum monitoring, electronic warfare, and cognitive radio applications, where low signal-to-noise ratio (SNR) conditions and the growing diversity of modulation schemes limit the performance of existing methods. This paper proposes an uncertainty-driven hybrid deep learning architecture for recognizing RF signals over a broad modulation space. The proposed approach carries out a multi-stage classification process by combining spectral information obtained through low-cost FFT-based preprocessing with time-frequency features extracted from short-time Fourier transform (STFT) spectrograms. The architecture comprises a 2D convolutional neural network (2D CNN)-based path for fast, low-latency primary classification, MC Dropout-supported Bayesian uncertainty estimation for assessing classification reliability, and a BiLSTM-based secondary decision mechanism activated under high-uncertainty conditions. The proposed system is evaluated in a controlled simulation environment spanning different SNR levels and modulation classes. Experimental results show that the primary 2D CNN path achieves $83.3\pm0.7\%$ accuracy with an inference time of only 0.138 ms per sample, providing superior performance compared with traditional rule-based and classical machine-learning approaches. Furthermore, the obtained findings reveal the limitations of compact spectral feature representations and classifiers lacking temporal modeling, particularly in disambiguating FSK-based modulations. The uncertainty estimation module offers promising results for detecting low-confidence decisions, and the proposed approach demonstrates the potential of a low-latency and scalable solution for real-time RF modulation recognition.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

Earth Observation regression tasks such as building height, canopy height, and above-ground biomass estimation underpin critical applications in urban planning, forest monitoring, and climate policy, where both accuracy and reliability are critical. Yet most deep learning models yield only deterministic predictions, providing no indication of per-pixel reliability. These regression tasks are inherently challenging due to heterogeneous land surfaces, skewed target distributions, sensor noise, and signal saturation at high target values, making uncertainty (UC) estimation essential for reliable inference. We address this gap by modeling aleatoric uncertainty using year-long Sentinel-1 SAR and Sentinel-2 MSI time series, proposing two complementary approaches: (i) Gaussian UC, which jointly predicts mean and standard deviation under a Gaussian assumption, and (ii) Quantile UC, which estimates the 10th, 50th, and 90th quantiles to capture asymmetric and heteroscedastic error distributions. Both models are evaluated on three representative EO regression tasks at 10 m spatial resolution. Results show that both approaches match or surpass deterministic benchmarks and existing global products, while delivering well-calibrated, interpretable, and operationally useful confidence estimates. Notably, both models outperform the current 10 m state-of-the-art uncertainty-aware model for canopy height estimation. Our implementation will be available at: https://github.com/RituYadav92/EO-Regression-Uncertainty-Estimation

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

We consider an open-world planning setting in which service robots must operate in unknown environments with incomplete knowledge of objects and actions. Traditional closed-world approaches with pre-programmed knowledge bases fail when robots encounter unexpected situations and tasks, posing a fundamental challenge for autonomous knowledge expansion in human environments. In this work, we propose an open-world planning framework that enables robots to automatically generate, verify, and update hypotheses about their abstract world models. Our key insight is to explicitly maintain uncertainty-aware knowledge expansion and integrate hypothesis verification into goal-reaching planning. The framework leverages foundation models to generate initial hypotheses over states and transitions, and applies automated planning to produce action sequences that jointly address hypothesis verification and task execution. Through iterative execution and refinement, the robot expands its knowledge by incorporating verification feedback from the foundation models when hypotheses prove incorrect. Extensive experiments in simulated and real-world environments demonstrate that our framework enables autonomous knowledge expansion and effective operation in open-world settings. These results indicate that integrating uncertainty-aware model expansion from robot foundation models with planning advances the practical deployment of household service robots.

Self-paced learning (SPL) is an effective learning paradigm that simulates the human learning process by progressing from easy to difficult samples based on the value of the loss function during the learning process. It has shown great potential in improving model performance and training efficiency. However, the prediction results of samples with smaller loss values are not necessarily reliable, indicating that such samples are not always simple samples for the model. Hence, this article proposes an uncertainty-aware self-paced learning based on evidential neural networks, termed UASPL, which integrates predictive reliability into sample selection through a general loss function within the Subjective Logic framework. This loss function incorporates uncertainty estimation and can be extended to different variants of SPL. Moreover, this loss function couples a sample selection preference, thereby ensuring the interpretability of the sample selection process. Finally, the experimental results on multiple datasets show that UASPL outperforms other SPL methods in terms of classification performance, interpretability, and generality. The source code is available at: https://github.com/treelife979/UASPL.

Active learning is a promising framework for reducing annotation costs in large-scale bioacoustic monitoring, where expert labeling is expensive and data distributions are highly heterogeneous across environments. However, existing sample selection strategies often rely on static criteria that do not adapt to the evolving reliability of model predictions during training. This limitation can lead to suboptimal exploration-exploitation trade-offs and redundant sample selection. We propose an active learning strategy for multilabel bioacoustic event classification that jointly models predictive uncertainty, embedding-space diversity, and intra-batch redundancy. The method introduces an adaptive weighting scheme that progressively shifts from diversity-driven exploration in high-uncertainty regimes toward uncertainty-driven exploitation as the model becomes more confident, reflecting the increasing reliability of the classifier. To further improve annotation efficiency, a greedy Maximum Marginal Relevance (MMR) procedure is used to enforce diversity among selected samples within each acquisition batch. We evaluate the proposed approach within the BioDCASE 2026 Task 4 active learning framework on terrestrial (BirdSet) and marine (ATBFL) benchmarks using pretrained audio embeddings and a fixed annotation budget. Experimental results show consistent improvements in learning efficiency and competitive in terms of macro mean Average Precision (mAP) and Area Under the Learning Curve (AULC) across heterogeneous acoustic domains. The gains are particularly pronounced on structured terrestrial soundscapes, while performance remains competitive under noisier marine conditions. These findings demonstrate that adaptive acquisition strategies combining uncertainty estimation, embedding-space diversity, and redundancy-aware batch construction provide an effective and robust solution for [...].

Certified world models estimate how long their predictions remain valid. We turn this validity horizon into an operational sensing clock: a rule for when an agent should stop coasting and re-sense. Starting from an audited equivariant world model, we derive a deadline for no-sensing intervals and show that deployable deadlines in learned world models must be drift-aware: on-manifold Lyapunov rates alone overestimate coasting validity, while calibrated native rollout-drift envelopes carry the deployed guarantee. On a frozen 3D VN-JEPA model, the resulting clock controls held-out interval-simultaneous certificate violation across seeds and data shards. In a cue-conditioned theorem-bed (a synthetic bench where all schedulers share the exact model, isolating the scheduling rule), the clock remains valid on the deployment distribution and substantially reduces eventful-tail violations relative to exact-mixture expected-belief scheduling at matched sensing budget. We also report limits: in the short-horizon frozen VN-JEPA regime, empirical conformal horizons match the deployed clock on validity and budget, and a partial-reset exploration finds no clean budget-matched advantage for the spectral term. Thus the contribution is a certified sensing-clock primitive and drift-aware deployment method, not a claim that spectral clocks empirically dominate all non-spectral schedulers.

Robust robot autonomy depends on scene representations that remain stable enough to support localization, navigation, and downstream decision making in dynamic environments. Monocular Gaussian Splatting SLAM provides high-fidelity mapping, but current uncertainty-aware methods still treat dynamic regions largely as per-frame observations. This makes the representation effectively memoryless: when a pedestrian slows, pauses, or reappears after occlusion, the current frame may look static, allowing dynamic content to be absorbed into the map and leaving persistent ghosting artifacts. We argue that this failure reflects a representation-level mismatch. Dynamic-ness is not an instantaneous appearance property, but a temporal property defined by motion history. Building on this view, we introduce Motion Permanence: the principle that an object's dynamic identity should persist over time rather than be re-decided from each frame independently. We realize this principle in MoPe, a memory-aware uncertainty filter for monocular Gaussian mapping. MoPe propagates the historical dynamic posterior through geometry-consistent SE(3) warping and fuses it with current-frame evidence using bounded Bayesian log-odds updates. The resulting persistent posterior guides tracking, mapping, dynamic-aware Gaussian insertion, and Gaussian-level post-cleanup. On Wild-SLAM, Bonn, and TUM sequences, MoPe improves tracking robustness and reduces residual ghosting, with the strongest gains on dynamic-human scenes that most directly violate the memoryless assumption. These results show that maintaining temporal dynamic state inside the scene representation is a practical step toward more reliable representation-centric autonomy in changing real-world environments.

Reinforcement Learning (RL) has become a powerful paradigm for de novo molecular design, enabling Chemical Language Models (CLMs) to navigate and explore the chemical space while optimizing specific desired properties. However, the existing RL frameworks treat all scoring functions as deterministic oracles, neglecting the inherent uncertainty attached to the predictions of the different molecular properties. This can lead to the exploration of highly-uncertain regions of the chemical space, focusing on the generation of highly scored molecules which are poorly supported by the training data. This can destabilize the optimization process, yielding predictions that are far from their true values. We propose and compare two complementary ways of incorporating predictive uncertainty into RL. In the first one, uncertainty is treated as an additional optimization objective and incorporated along with the rest of the scoring functions, allowing the policy to trade off exploitation against reliability. Secondly, uncertainty is used to modulate policy updates, reducing the influence of molecules whose properties lie far outside the scoring function confidence domain. Both approaches were evaluated across three different settings: (i) a controlled model system, in which the prediction error is modeled as a Gaussian distribution, with a variance proportional to the distance to the training data; and two real-world tasks, making use of (ii) ChemProp models and (iii) a Conformal Prediction wrapper applied to a Random forest classifier. We show that uncertainty-aware RL enables CLMs to explore chemical space more robustly by favoring lower-uncertainty regions. This leads to more reliable hit discovery without compromising molecular score, increasing the true hit rate by 0.25 (from 0.5 to 0.75), and nearly doubling the total number of true hits.

Autonomous vehicles must plan trajectories that satisfy a multitude of requirements on safety, passenger comfort, and compliance with traffic rules. However, in safety-critical scenarios, it is not always possible to satisfy all requirements simultaneously, necessitating their prioritization based on importance. At the same time, in these safety-critical scenarios, the uncertainty in trajectory predictions of the surrounding traffic, such as other vehicles and pedestrians, should be explicitly accounted for. In this work, we propose an uncertainty-aware trajectory planning framework that incorporates a predefined lexicographic ordering over Signal Temporal Logic (STL) specifications that stays valid under uncertainty. We implement this formulation with Model Predictive Path Integral (MPPI) control and we demonstrate the effectiveness of our method on simulation scenarios, showing that our framework efficiently handles conflicting objectives under realistic multi-modal uncertainty.

Geosteering requires navigating a well trajectory through an unknown geological configuration, while sequentially updating decisions based on indirect measurements acquired during drilling. This work presents an uncertainty-aware geosteering framework that tightly integrates particle filtering for probabilistic subsurface interpretation with value-based reinforcement learning for sequential decision-making. Geological uncertainty ahead of the drill bit is represented explicitly through a particle filter (PF), enabling belief-informed control rather than deterministic trajectory correction. The framework couples PF belief updates with belief-informed decision policies and evaluates three decision-making options that operate under identical uncertainty representations: an interpretable Approximate Dynamic Programming (ADP) scheme, a Deep Q-learning baseline, and a Dual Deep Reinforcement Learning (Dual DRL) architecture trained with a target Q-network scheme for stability, using a dueling (value/advantage) decomposition for Q-value parameterization. Beyond final placement performance, we assess policy behavior using stability-oriented metrics that quantify steering smoothness over time, providing additional operational insight into how decision policies respond as uncertainty evolves. The framework is integrated with an API for validation within an industrial geosteering simulator under realistic measurement noise and drilling constraints. Using identical geological realizations, operational limits, and reward definitions across methods, the experiments provide a controlled and high-fidelity evaluation of how alternative decision policies behave throughout the drilling process, rather than evaluating performance solely from the final well trajectory.

Large language models increasingly express uncertainty through natural-language statements, yet these expressions often fail to reflect the model's sampled behavior. We study verbal uncertainty alignment as a distributional calibration problem: the appropriate uncertainty target for a prompt should be estimated from repeated model outputs rather than from an isolated response. However, group rollouts alone are insufficient, since the resulting target must provide a useful training signal. Existing targets only partially satisfy this requirement. We propose SAGE, Semantic-Answer Guided Entropy, a group-level uncertainty target that constructs an answer-conditioned uncertainty geometry over sampled responses. SAGE preserves categorical, numeric, and symbolic answer distinctions while maintaining a smooth and scale-preserving calibration signal. We further apply this target through Group-Uncertainty Preference Optimization, or GUPO, an uncertainty-channel training framework that supervises verbal uncertainty expressions rather than the full response. Experiments across factual, mathematical, and multiple-choice reasoning tasks show improved uncertainty ranking, lower calibration error, and reduced overconfidence.

Radio frequency wireless power transfer (RF-WPT) is an enabling technology for supporting uninterrupted communications in future Internet of Things systems by reducing the need for battery replacement and mitigating battery-waste-related issues. For large-scale RF-WPT deployment, one of the main challenges is the scheduler-level resource allocation. Specifically, the transmitter must decide how much energy to deliver, when, and to whom, under limited charging resources, incomplete receiver-side information, and uncertain near-future charging conditions. This article positions generative artificial intelligence (GenAI) as a promising tool for this setting because it can foresee multiple plausible charging scenarios conditioned on coarse operational context and receiver-side information. We propose GenAI to act as an uncertainty-aware support layer for the RF-WPT scheduler rather than as a standalone forecasting or decision-making tool. To this end, we first revisit the main challenges of RF-WPT scheduling, and discuss how major GenAI families can support uncertainty-aware charging decisions by generating scenario-based inputs for downstream tasks. We then present a warehouse-style case study showing that preserving uncertainty through the sampling capability of generative models can improve robust charging decisions compared with deterministic prediction and simple non-learning baselines, especially under risk-sensitive objectives. Finally, we identify key open challenges and present some directions for future research.

Accurate lesion segmentation from whole-body Positron Emission Tomography (PET)/Computed Tomography (CT) scans is essential for cancer staging and treatment planning. PET provides functional metabolic information with different radiotracers, while CT offers anatomical localization. Lesion delineation from PET/CT imaging is clinically challenging due to subtle imaging features, confounders, and inter-reader variability. Existing deep learning approaches suffer from training-related stochasticity, inconsistent predictions, missed lesions in high tumor-burden cases, and lack uncertainty quantification, limiting their clinical reliability. Using nnU-Net as a baseline, we propose an uncertainty-aware framework for whole-body PET/CT lesion segmentation that integrates (1) Bayesian ensembling to reduce training stochasticity, (2) voxel-wise uncertainty quantification with epistemic and aleatoric decomposition, and (3) epistemic uncertainty-augmented training to improve lesion detection. Two public datasets, AutoPET-III (1,611 scans) and Deep-PSMA (200 scans), comprising FDG and PSMA studies across multiple cancer types, are used for training and evaluation. Bayesian ensembling improves robustness and performance over deterministic nnU-Net models on the unseen AutoPET-III test set. Uncertainty maps highlight regions of model disagreement and correlate with misclassifications, particularly false positives. Uncertainty-augmented training improves lesion recovery at the cost of increased FPVol, reflecting a precision-recall trade-off. A case-adaptive routing strategy further improves Dice by selecting between the base and augmented models. To our knowledge, this is the first study to systematically investigate uncertainty quantification in multi-tracer, pan-cancer PET/CT segmentation and to combine Bayesian ensembling with uncertainty-aware modeling for this task.

Designing a neural network processor is an end-to-end co-design problem: network architecture and training budget determine the inference workload; hardware mapping decisions determine chip area, latency, and energy; and these characteristics govern fabrication yield and manufacturing cost. In practice, these decisions are made in separate stages, and existing co-design methodologies are tightly coupled to specific algorithms, making it difficult to improve one component without reworking the entire pipeline. This paper presents a unified framework, grounded in monotone co-design theory, that composes four interoperable design blocks spanning network training, chip mapping, wafer-level fabrication, and compute resource allocation. Each block exposes only a functionality-resource interface to the rest of the system, so any block can be refined without structural changes elsewhere. A central contribution is the treatment of uncertainty: rather than collapsing stochastic outcomes into point estimates, the framework introduces Confidence, the inverse of success probability, as an explicit and optimizable resource alongside cost, time, and power. Three case studies validate the approach. The first recovers Pareto-optimal implementations across heterogeneous application scenarios. The second confirms that Confidence functions as a continuously tunable design knob rather than a post-hoc diagnostic. The third demonstrates that improving a single block's implementation set automatically propagates to the global Pareto front, without modifying the co-design diagram.

Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings. However, modern-sized datasets have made overparameterized deep networks the preferred methods of choice due to their predictive power and favorable computational scaling. While many posterior approximations exist, all incur approximation errors. Recent work accounts for this error in the form of computational uncertainty but comes at the cost of quadratic complexity and assumes fixed model hyperparameters. Here we extend this development to model selection, including a novel training loss and optimization scheme, which yields tractable inference in large state-spaces. We introduce a framework, the Computation-Aware State-Space Model (CASSM), specifically designed for the scale-imbalanced regime, where the number of trials is significantly lower than the number of recorded neurons. In this regime, for both synthetic and real data, we show that our method is competitive with data-hungry deep networks, with significantly improved uncertainty calibration over previous attempts to scale Bayesian methods. Our experiments provide a roadmap to neuroscience researchers in choosing from a host of potential dynamical latent variable models given key dataset properties and constraints.

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Reliable uncertainty quantification in continuous-time (CT) representation learning remains nascent, particularly within CT attention literature. We introduce the Neuronal Stochastic Attention Circuit (NSAC), a novel biologically-inspired CT attention architecture that reformulates attention logit computation as the solution of an Ornstein-Uhlenbeck stochastic differential equation modulated by input-dependent, nonlinear interlinked gates derived from repurposed C. elegans Neuronal Circuit Policies (NCPs) wiring mechanism. It induces a Gaussian distribution over logits that propagates principled stochasticity through a logistic-normal distribution over attention weights to yield probabilistic output. A two-term objective function combining Gaussian negative log-likelihood with an epistemic-separation regularizer enforces higher predictive variance under distributional shifts and enables joint quantification of aleatoric and epistemic uncertainty. Theoretically, we provide: (i) state stability bounds; (ii) closed-form guarantees; and (iii) frozen-coefficient error approximation. Empirically, we implement NSAC in a diverse set of learning tasks including: (i) irregular CT function approximation; (ii) multivariate regression; (iii) long-range forecasting; (iv) Industry 4.0; and (v) lane-keeping of autonomous vehicles. We observe that NSAC remains competitive against several baselines in terms of accuracy and produces informative uncertainty estimates while being interpretable at the neuronal cell level.

Guided Soft Actor-Critic (GSAC) distills knowledge from a privileged full-state teacher to a partial-observation student for autonomous driving, but uses a fixed distillation coefficient lambda regardless of the agent's uncertainty. We present Belief-Aware GSAC (BA-GSAC), which modulates lambda via ensemble disagreement, and use it as a testbed for a systematic empirical study asking: when does adaptive guidance actually help? Evaluating five strategies (fixed lambda in {0.01, 0.1}, adaptive, linear decay, and vanilla SAC) across three POMDP difficulty levels on Highway-Env, we find that preliminary single-seed runs suggest benefits under mild and moderate partial observability, but under severe occlusion (evaluated with 3 seeds for all methods) the adaptive coefficient collapses to lambda_min within about 3K steps. We trace this to an observability blindness phenomenon: because the ensemble predicts partial observations, it achieves low disagreement even under heavy occlusion, modeling what is visible but unable to detect what is missing. We diagnose the root cause and propose an architectural fix (training the ensemble on full-state predictions using the guiding actor's privileged access); while not validated here, we show that even with current limitations, the warmup phase provides measurable stabilization (CV=13.3% vs. 29.8% for constant lambda=0.01). In fact, a simple deterministic linear decay schedule achieves the best severe-POMDP performance across all metrics (mean 116.5, CV=8.9%), suggesting that the scheduling effect, not the ensemble, drives the stability benefit. These findings provide practical guidance for designing uncertainty-aware teacher-student frameworks and highlight ensemble prediction targets as an important design choice.

Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

In high-stakes automated decision-making, access to predictive uncertainty is essential for enabling users -- human or downstream systems -- to accept or reject predictions based on application-specific cost trade-offs. Such uncertainty-augmented (UA) systems -- i.e., systems that output both predictions and uncertainty scores -- are currently being assessed in the literature in a variety of ways, using separate metrics to evaluate the predictions and the uncertainty scores, setting a cost function with a fixed rejection cost or integrating over a coverage-risk curve. We argue that these evaluation approaches are inadequate for assessing overall performance of the UA system for decision making under uncertainty and propose a novel family of metrics, ECUAS$_n$, formulated as proper scoring rules for the task of interest. The parameter $n$ controls the trade-off between the cost of incorrect predictions and imperfect uncertainties depending on the needs of the use-case. We demonstrate the advantages of the ECUAS$_n$ metrics both theoretically and empirically, through experiments on diverse classification and generation datasets, including a manually annotated subset of TriviaQA.

Carotid atherosclerosis is a major contributor to ischemic stroke and transient ischemic attack. Conventional ultrasound assessment is commonly based on intima-media thickness, plaque appearance, stenosis degree, and peak systolic velocity, but these morphology- and velocity-based indicators may not fully capture patient-specific vascular risk. This study presents AtheroFlow-XNet, a CUBS-compatible ultrasound morphology and uncertainty-aware learning baseline for carotid intima-media segmentation and preliminary risk prediction. Using the Carotid Ultrasound Boundary Study dataset, manual lumen-intima and media-adventitia boundary annotations were converted into dense intima-media masks for supervised segmentation. Clinical variables were incorporated into an auxiliary risk-prediction branch, and Monte Carlo dropout was used for uncertainty-aware inference. The model was evaluated using a patient-level train-validation-test split with 1,522 training images, 326 validation images, and 328 testing images. The proposed model achieved a Dice coefficient of 0.7930 for LI-MA mask segmentation, a segmentation loss of 0.2359, and an area under the receiver operating characteristic curve of 0.6910 for preliminary risk prediction. Qualitative results showed that predicted masks were generally aligned with manual annotations, while uncertainty maps highlighted ambiguous wall-boundary regions. These results suggest that ultrasound-derived carotid morphology can support automated wall analysis and uncertainty-aware interpretation. Since CUBS does not provide Doppler waveforms or CFD-derived hemodynamic biomarkers, this work should be interpreted as a reproducible morphology-driven baseline. Future work will incorporate Doppler-derived flow profiles, patient-specific vascular reconstruction, and CFD-based wall shear biomarkers.

In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the \textit{avoiding undesired future} (AUF) problem. To address this, the \textit{rehearsal learning} framework has been proposed to model influence relations for effective decisions. However, existing rehearsal methods rely on restrictive parametric assumptions such as linear systems or additive noise, limiting their practical applicability. In this paper, we propose the first non-parametric rehearsal learning approach for AUF without assuming specific functional forms of data generation processes. Specifically, we use kernel machinery to reformulate the AUF objective into a unified representation that disentangles desirability modeling from action-induced distributional changes. To handle the discontinuity of desirability indicator, we present a smooth Probit surrogate and provide an approximation error bound. Meanwhile, we capture the action-induced changes via conditional mean embeddings, and develop a kernel ridge regression based nested estimator for AUF objective with consistency guarantees. Such a formulation naturally accommodates nonlinear systems and non-additive noise, and empirical results on synthetic and real-data-derived semi-synthetic benchmarks demonstrate the effectiveness and flexibility of our approach.

A key strategy for balancing performance and cost in modern machine learning systems is to dynamically route queries to either a low-cost model or a more expensive oracle (such as a large pretrained model or human expert), an approach known as model routing. In this work we present a new uncertainty-aware router that (1) avoids unnecessary oracle calls on inherently ambiguous queries, and (2) adapts dynamically to different loss functions and cost parameters through simple hyperparameter changes, without retraining. Our method, applicable to any classification setting where multiple independent annotations per input are available, is based on decomposing total uncertainty into irreducible and reducible components using higher-order predictors [Ahdritz et al., 2025]. This enables a unified approach to both routing and abstention: predict with the weak model when uncertainty is low, route to the oracle when reducible uncertainty is high, and abstain when irreducible uncertainty is high. Our router comes with strong theoretical guarantees bounding regret relative to optimal task-specific routers. We conduct experiments on both synthetic and real-world datasets that demonstrate the benefits of our approach in suitable regimes -- in particular, whenever reducible and irreducible uncertainty are not too correlated.

Knowledge Tracing (KT) is fundamental to intelligent education systems, yet relies on educational logs that are selectively observed. The non-random nature of exercise recommendations and student choices inevitably induces severe selection bias. Most existing KT methods neglect this issue, training on observed logs using standard empirical risk, which yields biased mastery estimates and accumulates errors in subsequent recommendations. To address this, we introduce a doubly robust (DR) formulation for KT that integrates a propensity model with an error imputation model, theoretically guaranteeing unbiasedness if either model is accurate. Beyond unbiasedness, in the sequential setting of KT, we identify that the estimator's performance is compromised by variance-dependent stochastic deviations that accumulate over time, thereby causing training instability and limiting performance. To mitigate this, we derive a generalization bound that explicitly characterizes the impact of estimator variance and identifies temporal smoothness as a key factor in controlling it. Building on these theoretical insights, we propose the Temporal Smoothness Doubly Robust (TSDR) framework. TSDR jointly optimizes the KT predictor and the imputation model with a smoothness regularizer, effectively reducing variance while preserving the unbiasedness guarantee of DR. Experiments on multiple real-world benchmarks demonstrate that TSDR consistently enhances various state-of-the-art KT backbones, underscoring the vital role of principled bias correction in KT.

Visual affordances identify regions in an image with potential interactions, offering a novel paradigm for scene understanding. Recognizing affordances allows autonomous robots to act more naturally, could enhance human-robot interactions, enrich augmented reality systems, and benefit prosthetic vision devices. Accurate and localized prediction of affordance regions, rather than general saliency maps is crucial for these applications. We present a model for instance segmentation of affordances by adopting sample-based and ensembles approaches for uncertainty estimation. We extend an attention-based architecture for our novel task, showing with detailed ablation experiments the effects of each component. By comparing the distribution of these different detections, we extract pixel-wise epistemic and aleatoric variances at both the semantic and spatial levels. In addition, we propose a novel measure called Probability-based Mask Quality, which enables a comprehensive analysis of semantic and spatial variations in a probabilistic instance segmentation model. Our results show that the global consensus of multiple sub-networks of Bayesian models improve deterministic networks due to a better mask refinement and generalization. This fact, joined with the more powerful features extracted by attention-based mechanisms, represent an improvement of +7.4 p.p on the $F_β^w$ score in the challenging IIT-Aff dataset. Bayesian models are also better calibrated, producing less overconfident probabilities and with a better uncertainty estimation. Qualitative results show that aleatoric variance appears in the contour of the objects, while the epistemic variance is observed in visual challenging pixels, adding interpretability to the neural network.

The effectiveness of active learning hinges on the choice of the acquisition criterion by which a learning algorithm selects potentially informative data points whose label is subsequently queried. This paper proposes a novel gradient-based acquisition criterion, derived from a generalization bound introduced by Luo et al. (2022). This criterion can be applied in lieu of uncertainty measures in uncertainty sampling, or incorporated into diversity-based methods that consider the spread of sampled points in addition to the uncertainty of their labels. We provide a theoretical justification of the proposed acquisition criterion, and demonstrate its effectiveness in an empirical evaluation.

We address the problem of searching for an unknown number of stationary targets at unknown positions with a mobile agent. A probability hypothesis density filter is used to estimate the expected number of targets under measurement uncertainty. Existing planners, such as Active Search (AS) and its Intermittent variant (ASI), achieve accurate detection but require costly online optimization. To reduce online computation, we propose to use a convolutional neural network to approximate AS or ASI decisions through direct inference. The network is trained on AS/ASI data using a multi-channel grid that encodes target beliefs, the agent position, visitation history, and boundary information. Simulations with uniform and clustered target distributions show that the network achieves detection rates comparable to AS or ASI while reducing computation by orders of magnitude.

Complex-Valued Neural Networks (CVNNs) have significant advantages in handling tasks that involve complex numbers. However, existing CVNNs are unable to quantify predictive uncertainty. We propose, for the first time, dropout-based Bayesian Complex-Valued Neural Networks (BayesCVNNs) to enable uncertainty quantification for complex-valued applications, exhibiting broad applicability and efficiency for hardware implementation due to modularity. Furthermore, as the dual-part nature of complex values significantly broadens the design space and enables novel configurations based on layer-mixing and part-mixing, we introduce an automated search approach to effectively identify optimal configurations for both real and imaginary components. To facilitate deployment, we present a framework that generates customized FPGA-based accelerators for BayesCVNNs, leveraging a set of optimized building blocks. Experiments demonstrate the best configuration can be effectively found via the automated search, attaining higher performance with lower hardware costs compared with manually crafted models. The optimized accelerators achieve approximately 4.5x and 13x speedups on different models with less than 10% power consumption compared to GPU implementations, and outperform existing work in both algorithm and hardware aspects. Our code is publicly available at: https://github.com/zehuanzhang/BayesCVNN.git.

Learning Path Recommendation (LPR) is critical for personalized education, yet current methods often fail to account for historical interaction uncertainty (e.g., lucky guesses or accidental slips) and lack adaptability to diverse learning goals. We propose U-GLAD (Uncertainty-aware Generative Learning Path Recommendation with Cognition-Adaptive Diffusion). To address representation bias, the framework models cognitive states as probability distributions, capturing the learner's underlying true state via a Gaussian LSTM. To ensure highly personalized recommendation, a goal-oriented concept encoder utilizes multi-head attention and objective-specific transformations to dynamically align concept semantics with individual learning goals, generating uniquely tailored embeddings. Unlike traditional discriminative ranking approaches, our model employs a generative diffusion model to predict the latent representation of the next optimal concept. Extensive evaluations on three public datasets demonstrate that U-GLAD significantly outperforms representative baselines. Further analyses confirm its superior capability in perceiving interaction uncertainty and providing stable, goal-driven recommendation paths.

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning--optimization systems.

In classical Informative Path Planning (C-IPP), robots are typically modeled as mobile sensors that acquire digital measurements such as images or radiation levels. In this model, since making a measurement leaves the robot's physical state unchanged, the cost of traversing an edge remains static regardless of when it is traversed. This is a natural assumption for many missions, but does not extend to settings involving physical sample collection, where each collected sample adds mass and increases the energy cost of all subsequent motion. As a result, IPP formulations that ignore this coupling between information gain and load-dependent traversal cost can produce plans that are distance-efficient but energy-suboptimal, collecting fewer samples and less data than the energy budget would permit. In this paper, we first introduce Load-aware Informative Path Planning (LIPP), a strict generalization of C-IPP that explicitly models this coupling, with C-IPP recovered as the special case of zero sample mass. We then formulate LIPP as a Mixed-Integer Quadratic Program (MIQP) that jointly optimizes visitation location, order, and per-location sampling count under an energy budget. We further derive theoretical bounds on the path-length increase of LIPP relative to C-IPP, characterizing the trade-off for improved energy efficiency. Finally, through extensive simulations across 2,000 diverse mission scenarios, we demonstrate that LIPP progressively achieves higher uncertainty reduction per unit energy as sample mass increases.

Inertial measurement units (IMUs), which provide high-frequency linear acceleration and angular velocity measurements, serve as fundamental sensing modalities in robotic systems. Recent advances in deep neural networks have led to remarkable progress in inertial odometry. However, the heavy reliance on ground truth data during training fundamentally limits scalability and generalization to unseen and diverse environments. We propose KISS-IMU, a novel self-supervised inertial odometry framework that eliminates ground truth dependency by leveraging simple LiDAR-based ICP registration and pose graph optimization as a supervisory signal. Our approach embodies two key principles: keeping the IMU stable through motion-aware balanced training and keeping the IMU strong through uncertainty-driven adaptive weighting during inference. To evaluate performance across diverse motion patterns and scenarios, we conducted comprehensive experiments on various real-world platforms, including quadruped robots. Importantly, we train only the IMU network in a self-supervised manner, with LiDAR serving solely as a lightweight supervisory signal rather than requiring additional learnable processes. This design enables the framework to ensure robustness without relying on joint multi-modal learning or ground truth supervision. The supplementary materials are available at https://sparolab.github.io/research/kiss_imu.

We pose uncertainty quantification and exploration in online decision-making as a problem of training and generation from an autoregressive sequence model, an area experiencing rapid innovation. Our approach rests on viewing uncertainty as arising from missing future outcomes that could be revealed through action choices, rather than from unobservable latent parameters of the environment. This reformulation aligns naturally with modern machine learning capabilities: we can i) train generative models through next-outcome prediction rather than fit explicit priors, ii) assess uncertainty through autoregressive generation rather than sampling latent parameters from posteriors, and iii) adapt to new information by extending the sequence model's context rather than explicit posterior updating. Our main theoretical result establishes a reduction from online decision-making to offline next-outcome prediction: Bayesian regret is controlled directly by the sequence model's offline prediction loss, without requiring an explicit latent-variable posterior. Experiments, including a semi-synthetic news recommendation task, show that autoregressive generation produces calibrated epistemic uncertainty and enables effective exploration by using article text as prior information to focus exploration on resolving remaining uncertainties.