Crowdsourcing enables scalable autonomous driving map construction, but low-cost sensor noise hinders quality from improving with data volume. We propose CSMapping, a system that produces accurate semantic maps and topological road centerlines whose quality consistently increases with more crowdsourced data. For semantic mapping, we train a latent diffusion model on HD maps (optionally conditioned on SD maps) to learn a generative prior of real-world map structure, without requiring paired crowdsourced/HD-map supervision. This prior is incorporated via constrained MAP optimization in latent space, ensuring robustness to severe noise and plausible completion in unobserved areas. Initialization uses a robust vectorized mapping module followed by diffusion inversion; optimization employs efficient Gaussian-basis reparameterization, projected gradient descent zobracket multi-start, and latent-space factor-graph for global consistency. For topological mapping, we apply confidence-weighted k-medoids clustering and kinematic refinement to trajectories, yielding smooth, human-like centerlines robust to trajectory variation. Experiments on nuScenes, Argoverse 2, and a large proprietary dataset achieve state-of-the-art semantic and topological mapping performance, with thorough ablation and scalability studies.

Active inference proposes expected free energy as an objective for planning and decision-making to adequately balance exploitative and explorative drives in learning agents. The exploitative drive, or what an agent wants to achieve, is formalised as the Kullback-Leibler divergence between a variational probability distribution, updated at each inference step, and a preference probability distribution that indicates what states or observations are more likely for the agent, hence determining the agent's goal in a certain environment. In the literature, the questions of how the preference distribution should be specified and of how a certain specification impacts inference and learning in an active inference agent have been given hardly any attention. In this work, we consider four possible ways of defining the preference distribution, either providing the agents with hard or soft goals and either involving or not goal shaping (i.e., intermediate goals). We compare the performances of four agents, each given one of the possible preference distributions, in a grid world navigation task. Our results show that goal shaping enables the best performance overall (i.e., it promotes exploitation) while sacrificing learning about the environment's transition dynamics (i.e., it hampers exploration).

Reliable real-time analysis of sensor data is essential for structural health monitoring (SHM) of high-value assets, yet a major challenge is to obtain spatially resolved full-field aleatoric and epistemic uncertainties for trustworthy decision-making. We present an integrated SHM framework that combines principal component analysis (PCA), a Bayesian neural network (BNN), and Hamiltonian Monte Carlo (HMC) inference, mapping sparse strain gauge measurements onto leading PCA modes to reconstruct full-field strain distributions with uncertainty quantification. The framework was validated through cyclic four-point bending tests on carbon fiber reinforced polymer (CFRP) specimens with varying crack lengths, achieving accurate strain field reconstruction (R squared value > 0.9) while simultaneously producing real-time uncertainty fields. A key contribution is that the BNN yields robust full-field strain reconstructions from noisy experimental data with crack-induced strain singularities, while also providing explicit representations of two complementary uncertainty fields. Considered jointly in full-field form, the aleatoric and epistemic uncertainty fields make it possible to diagnose at a local level, whether low-confidence regions are driven by data-inherent issues or by model-related limitations, thereby supporting reliable decision-making. Collectively, the results demonstrate that the proposed framework advances SHM toward trustworthy digital twin deployment and risk-aware structural diagnostics.

Loss of lung function in cystic fibrosis (CF) occurs progressively, punctuated by acute pulmonary exacerbations (PEx) in which abrupt declines in lung function are not fully recovered. A key component of CF management over the past half century has been the treatment of PEx to slow lung function decline. This has been credited with improvements in survival for people with CF (PwCF), but there is no consensus on the optimal approach to PEx management. BEAT-CF (Bayesian evidence-adaptive treatment of CF) was established to build an evidence-informed knowledge base for CF management. The BEAT-CF causal model is a directed acyclic graph (DAG) and Bayesian network (BN) for PEx that aims to inform the design and analysis of clinical trials comparing the effectiveness of alternative approaches to PEx management. The causal model describes relationships between background risk factors, treatments, and pathogen colonisation of the airways that affect the outcome of an individual PEx episode. The key factors, outcomes, and causal relationships were elicited from CF clinical experts and together represent current expert understanding of the pathophysiology of a PEx episode, guiding the design of data collection and studies and enabling causal inference. Here, we present the DAG that documents this understanding, along with the processes used in its development, providing transparency around our trial design and study processes, as well as a reusable framework for others.

This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.

Diffusion models achieve high-quality image generation but are limited by slow iterative sampling. Distillation methods alleviate this by enabling one- or few-step generation. Flow matching, originally introduced as a distinct framework, has since been shown to be theoretically equivalent to diffusion under Gaussian assumptions, raising the question of whether distillation techniques such as score distillation transfer directly. We provide a simple derivation -- based on Bayes' rule and conditional expectations -- that unifies Gaussian diffusion and flow matching without relying on ODE/SDE formulations. Building on this view, we extend Score identity Distillation (SiD) to pretrained text-to-image flow-matching models, including SANA, SD3-Medium, SD3.5-Medium/Large, and FLUX.1-dev, all with DiT backbones. Experiments show that, with only modest flow-matching- and DiT-specific adjustments, SiD works out of the box across these models, in both data-free and data-aided settings, without requiring teacher finetuning or architectural changes. This provides the first systematic evidence that score distillation applies broadly to text-to-image flow matching models, resolving prior concerns about stability and soundness and unifying acceleration techniques across diffusion- and flow-based generators. A project page is available at https://yigu1008.github.io/SiD-DiT.

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this model to a fully probabilistic formulation introduces several design challenges. In particular, for tensor train (TT) models, it is unclear which TT-core should be treated in a Bayesian manner. We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core and employs variational inference (VI) for precision hyperparameters. Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training. The method's effectiveness is demonstrated on an inverse dynamics problem.

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Uncertainty quantification is essential for deploying reliable Graph Neural Networks (GNNs), where existing approaches primarily rely on Bayesian inference or ensembles. In this paper, we introduce the first credal graph neural networks (CGNNs), which extend credal learning to the graph domain by training GNNs to output set-valued predictions in the form of credal sets. To account for the distinctive nature of message passing in GNNs, we develop a complementary approach to credal learning that leverages different aspects of layer-wise information propagation. We assess our approach on uncertainty quantification in node classification under out-of-distribution conditions. Our analysis highlights the critical role of the graph homophily assumption in shaping the effectiveness of uncertainty estimates. Extensive experiments demonstrate that CGNNs deliver more reliable representations of epistemic uncertainty and achieve state-of-the-art performance under distributional shift on heterophilic graphs.