In this manuscript we introduce a novel Decision Flow (DF) framework for sampling from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous space, continuous time path Integral Diffusion sampling technique to discrete time and space, while also generalizing the Generative Flow Network framework. In its most basic form, an explicit, Neural Network (NN) free formulation, DF leverages the linear solvability of the the underlying MDP to adjust the transition probabilities of the prior sampler. The resulting Markov Process is expressed as a convolution of the reverse time Green's function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN based extensions, and outline how DF can enhance guided sampling across various applications.

This paper introduces the Heteroscedastic AddiVortes model, a Bayesian non-parametric regression framework that simultaneously models the conditional mean and variance of a response variable using adaptive Voronoi tessellations. By employing a sum-of-tessellations approach for the mean and a product-of-tessellations approach for the variance, the model provides a flexible and interpretable means to capture complex, predictor-dependent relationships and heteroscedastic patterns in data. This dual-layer representation enables precise inference, even in high-dimensional settings, while maintaining computational feasibility through efficient Markov Chain Monte Carlo (MCMC) sampling and conjugate prior structures. We illustrate the model's capability through both simulated and real-world datasets, demonstrating its ability to capture nuanced variance structures, provide reliable predictive uncertainty quantification, and highlight key predictors influencing both the mean response and its variability. Empirical results show that the Heteroscedastic AddiVortes model offers a substantial improvement in capturing distributional properties compared to both homoscedastic and heteroscedastic alternatives, making it a robust tool for complex regression problems in various applied settings.

Suppose we observe a trajectory of length $n$ from an $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary distribution of any such process on elements that occur with a certain frequency in the observed sequence. We estimate this vector of probabilities in total variation distance, showing universal consistency in $n$ and recovering known results for i.i.d. sequences as special cases. Our proposed methodology carefully combines the plug-in (or empirical) estimator with a recently-proposed modification of the Good--Turing estimator called WingIt, which was originally developed for Markovian sequences. En route to controlling the error of our estimator, we develop new performance bounds on WingIt and the plug-in estimator for $\alpha$-mixing stochastic processes. Importantly, the extensively used method of Poissonization can no longer be applied in our non i.i.d. setting, and so we develop complementary tools -- including concentration inequalities for a natural self-normalized statistic of mixing sequences -- that may prove independently useful in the design and analysis of estimators for related problems.

In real-life scenarios, a Reinforcement Learning (RL) agent aiming to maximise their reward, must often also behave in a safe manner, including at training time. Thus, much attention in recent years has been given to Safe RL, where an agent aims to learn an optimal policy among all policies that satisfy a given safety constraint. However, strict safety guarantees are often provided through approaches based on linear programming, and thus have limited scaling. In this paper we present a new, scalable method, which enjoys strict formal guarantees for Safe RL, in the case where the safety dynamics of the Markov Decision Process (MDP) are known, and safety is defined as an undiscounted probabilistic avoidance property. Our approach is based on state-augmentation of the MDP, and on the design of a shield that restricts the actions available to the agent. We show that our approach provides a strict formal safety guarantee that the agent stays safe at training and test time. Furthermore, we demonstrate that our approach is viable in practice through experimental evaluation.

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

Effectively understanding and managing CVD requires advanced diagnostic tools capable of accurately characterizing complex hemodynamics within the cardiovascular system. While medical imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI) provide high-resolution anatomical detail, they lack the capability to directly capture hemodynamics information (e.g., blood flow patterns, pressure, and wall shear stress fields) critical for understanding vascular function and pathology. To bridge this gap, image-based computational fluid dynamics (CFD) has emerged as a powerful computational paradigm that derives hemodynamic information from anatomical images via conservation laws. Although widely utilized in cardiovascular research, the clinical application of image-based CFD for diagnosis and surgical planning remains limited, largely due to the challenges associated with efficient and accurate model construction [2-4]. Constructing patient-specific vascular models for image-based CFD involves multiple steps, including image segmentation, geometry modeling, and mesh generation for the computational domain, all of which are critical to ensuring the fidelity of the final simulation results. However, the standard workflow heavily relies on manual methods, making it highly labor-intensive and time-consuming.

Ensuring safe interactions between autonomous vehicles (AVs) and human drivers in mixed traffic systems remains a major challenge, particularly in complex, high-risk scenarios. This paper presents a cognition-decision framework that integrates individual variability and commonalities in driver behavior to quantify risk cognition and model dynamic decision-making. First, a risk sensitivity model based on a multivariate Gaussian distribution is developed to characterize individual differences in risk cognition. Then, a cognitive decision-making model based on the drift diffusion model (DDM) is introduced to capture common decision-making mechanisms in highrisk environments. The DDM dynamically adjusts decision thresholds by integrating initial bias, drift rate, and boundary parameters, adapting to variations in speed, relative distance, and risk sensitivity to reflect diverse driving styles and risk preferences. By simulating high-risk scenarios with lateral, longitudinal, and multidimensional risk sources in a driving simulator, the proposed model accurately predicts cognitive responses and decision behaviors during emergency maneuvers. Specifically, by incorporating driver-specific risk sensitivity, the model enables dynamic adjustments of key DDM parameters, allowing for personalized decision-making representations in diverse scenarios. Comparative analysis with IDM, Gipps, and MOBIL demonstrates that DDM more precisely captures human cognitive processes and adaptive decision-making in high-risk scenarios. These findings provide a theoretical basis for modeling human driving behavior and offer critical insights for enhancing AV-human interaction in real-world traffic environments. Introduction Driving safety is directly influenced by drivers' risk cognition and collision avoidance decisionmaking abilities in high-risk scenarios. In real-world driving, risk cognition generally involves complex interactions among multiple co-existing risk factors rather than being limited to a single risk source (Crosato et al., 2024; Huang et al., 2022).

Text-to-image latent diffusion models (LDMs) have recently emerged as powerful generative models with great potential for solving inverse problems in imaging. However, leveraging such models in a Plug & Play (PnP), zero-shot manner remains challenging because it requires identifying a suitable text prompt for the unknown image of interest. Also, existing text-to-image PnP approaches are highly computationally expensive. We herein address these challenges by proposing a novel PnP inference paradigm specifically designed for embedding generative models within stochastic inverse solvers, with special attention to Latent Consistency Models (LCMs), which distill LDMs into fast generators. We leverage our framework to propose LAtent consisTency INverse sOlver (LATINO), the first zero-shot PnP framework to solve inverse problems with priors encoded by LCMs. Our conditioning mechanism avoids automatic differentiation and reaches SOTA quality in as little as 8 neural function evaluations. As a result, LATINO delivers remarkably accurate solutions and is significantly more memory and computationally efficient than previous approaches. We then embed LATINO within an empirical Bayesian framework that automatically calibrates the text prompt from the observed measurements by marginal maximum likelihood estimation. Extensive experiments show that prompt self-calibration greatly improves estimation, allowing LATINO with PRompt Optimization to define new SOTAs in image reconstruction quality and computational efficiency.

Pursuit-evasion (PE) problem is a critical challenge in multi-robot systems (MRS). While reinforcement learning (RL) has shown its promise in addressing PE tasks, research has primarily focused on single-target pursuit, with limited exploration of multi-target encirclement, particularly in large-scale settings. This paper proposes a Transformer-Enhanced Reinforcement Learning (TERL) framework for large-scale multi-target encirclement. By integrating a transformer-based policy network with target selection, TERL enables robots to adaptively prioritize targets and safely coordinate robots. Results show that TERL outperforms existing RL-based methods in terms of encirclement success rate and task completion time, while maintaining good performance in large-scale scenarios. Notably, TERL, trained on small-scale scenarios (15 pursuers, 4 targets), generalizes effectively to large-scale settings (80 pursuers, 20 targets) without retraining, achieving a 100% success rate.

Studies in reward shaping for reinforcement learning (RL) have flourished in recent years due to its ability to speed up training. Our previous work proposed an adaptive potential function (APF) and showed that APF can accelerate the Q-learning with a Multi-layer Perceptron algorithm in the low-dimensional domain. This paper proposes to extend APF with an encoder (APF+) for RL state representation, allowing applying APF to the pixel-based Atari games using a state-encoding method that projects high-dimensional game's pixel frames to low-dimensional embeddings. We approach by designing the state-representation encoder as a W-shaped network (W-Net), by using which we are able to encode both the background as well as the moving entities in the game frames. Specifically, the embeddings derived from the pre-trained W-Net consist of two latent vectors: One represents the input state, and the other represents the deviation of the input state's representation from itself. We then incorporate W-Net into APF to train a downstream Dueling Deep Q-Network (DDQN), obtain the APF-WNet-DDQN, and demonstrate its effectiveness in Atari game-playing tasks. To evaluate the APF+W-Net module in such high-dimensional tasks, we compare with two types of baseline methods: (i) the basic DDQN; and (ii) two encoder-replaced APF-DDQN methods where we replace W-Net by (a) an unsupervised state representation method called Spatiotemporal Deep Infomax (ST-DIM) and (b) a ground truth state representation provided by the Atari Annotated RAM Interface (ARI). The experiment results show that out of 20 Atari games, APF-WNet-DDQN outperforms DDQN (14/20 games) and APF-STDIM-DDQN (13/20 games) significantly. In comparison against the APF-ARI-DDQN which employs embeddings directly of the detailed game-internal state information, the APF-WNet-DDQN achieves a comparable performance.