We introduce $Ψ$-Sampler, an SMC-based framework incorporating pCNL-based initial particle sampling for effective inference-time reward alignment with a score-based generative model. Inference-time reward alignment with score-based generative models has recently gained significant traction, following a broader paradigm shift from pre-training to post-training optimization. At the core of this trend is the application of Sequential Monte Carlo (SMC) to the denoising process. However, existing methods typically initialize particles from the Gaussian prior, which inadequately captures reward-relevant regions and results in reduced sampling efficiency. We demonstrate that initializing from the reward-aware posterior significantly improves alignment performance. To enable posterior sampling in high-dimensional latent spaces, we introduce the preconditioned Crank-Nicolson Langevin (pCNL) algorithm, which combines dimension-robust proposals with gradient-informed dynamics. This approach enables efficient and scalable posterior sampling and consistently improves performance across various reward alignment tasks, including layout-to-image generation, quantity-aware generation, and aesthetic-preference generation, as demonstrated in our experiments. Project Webpage: https://psi-sampler.github.io/

Simulation-based inference (SBI) offers a flexible and general approach to performing Bayesian inference: In SBI, a neural network is trained on synthetic data simulated from a model and used to rapidly infer posterior distributions for observed data. A key goal for SBI is to achieve accurate inference with as few simulations as possible, especially for expensive simulators. In this work, we address this challenge by repurposing recent probabilistic foundation models for tabular data: We show how tabular foundation models -- specifically TabPFN -- can be used as pre-trained autoregressive conditional density estimators for SBI. We propose Neural Posterior Estimation with Prior-data Fitted Networks (NPE-PFN) and show that it is competitive with current SBI approaches in terms of accuracy for both benchmark tasks and two complex scientific inverse problems. Crucially, it often substantially outperforms them in terms of simulation efficiency, sometimes requiring orders of magnitude fewer simulations. NPE-PFN eliminates the need for inference network selection, training, and hyperparameter tuning. We also show that it exhibits superior robustness to model misspecification and can be scaled to simulation budgets that exceed the context size limit of TabPFN. NPE-PFN provides a new direction for SBI, where training-free, general-purpose inference models offer efficient, easy-to-use, and flexible solutions for a wide range of stochastic inverse problems.

We introduce the Target Concrete Score Identity Sampler (TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a Continuous-Time Markov Chain (CTMC). Our approach builds on a forward in time CTMC with a uniform noising kernel and relies on the proposed Target Concrete Score Identity, which relates the concrete score, the ratio of marginal probabilities of two states, to a ratio of expectations of Boltzmann factors under the forward uniform diffusion kernel. This formulation enables Monte Carlo estimation of the concrete score without requiring samples from the target distribution or computation of the partition function. We approximate the concrete score with a neural network and propose two algorithms: Self-Normalized TCSIS and Unbiased TCSIS. Finally, we demonstrate the effectiveness of TCSIS on problems from statistical physics.

Abstract--Integrated sensing and communication (ISAC) enables simultaneous localization, environment perception, and data exchange for connected autonomous vehicles. T o overcome this limitation, we propose a planning-oriented ISAC (PISAC) framework that reduces the sensing uncertainty of planning-bottleneck obstacles and expands the safe navigable path for the ego-vehicle, thereby bridging the gap between physical-layer optimization and motion-level planning. The core of PISAC lies in deriving a closed-form safety bound that explicitly links ISAC transmit power to sensing uncertainty, based on the Cram er-Rao Bound and occupancy inflation principles. Using this model, we formulate a bilevel power allocation and motion planning (PAMP) problem, where the inner layer optimizes the ISAC beam power distribution and the outer layer computes a collision-free trajectory under uncertainty-aware safety constraints. Comprehensive simulations in high-fidelity urban driving environments demonstrate that PISAC achieves up to 40% higher success rates and over 5% shorter traversal times than existing ISAC-based and communication-oriented benchmarks, validating its effectiveness in enhancing both safety and efficiency.

Recent work has demonstrated the potential of diffusion models in robot bimanual skill learning. However, existing methods ignore the learning of posture-dependent task features, which are crucial for adapting dual-arm configurations to meet specific force and velocity requirements in dexterous bimanual manipulation. To address this limitation, we propose Manipulability-Aware Diffusion Policy (ManiDP), a novel imitation learning method that not only generates plausible bimanual trajectories, but also optimizes dual-arm configurations to better satisfy posture-dependent task requirements. ManiDP achieves this by extracting bimanual manipulability from expert demonstrations and encoding the encapsulated posture features using Riemannian-based probabilistic models. These encoded posture features are then incorporated into a conditional diffusion process to guide the generation of task-compatible bimanual motion sequences. We evaluate ManiDP on six real-world bimanual tasks, where the experimental results demonstrate a 39.33$\%$ increase in average manipulation success rate and a 0.45 improvement in task compatibility compared to baseline methods. This work highlights the importance of integrating posture-relevant robotic priors into bimanual skill diffusion to enable human-like adaptability and dexterity.

Complex events such as wildfires, floods, and heatwaves are no longer isolated phenomena but interlinked hazards that propagate through interconnected infrastructure networks. When one system fails, others that depend on it often cascade toward collapse, producing widespread disruption and social inequity. Recent crises including the 2023 Vermont flooding, the 2024 Texas winter freeze, and the 2025 Southern California wildfire illustrate how climate - amplified events can simultaneously strain energy, water, communication, and transportation systems. Traditional risk assessments, which often treat hazards as discrete and static events, are insufficient to capture the evolving and compounding nature of modern disasters. Digital Twin (DT) technology offers a promising avenue for improving situational awareness and decision - making under such conditions. Originally introduced for aerospace engineering and later adopted across industrial sectors, DTs create real - time virtual counterparts of physical systems using sensor data, predictive modeling, and feedback control (Grieves & Vickers, 2018; Tao et al., 2019) . Within the built environment, DTs have been applied to asset monitoring, predictive maintenance, and urban system management (Errandonea et al., 2020; Fogli, 2019; Fuller et al., 2020) . However, most conventional DTs rely on stable connectivity, complete datasets, and deterministic control assumptions that are not held during crises characterized by cascading failures and data disruption. To address these challenges, the concept of the Risk - Informed Digital Twin (RDT) integrates probabilistic modeling, uncertainty quantification, and decision support within the DT architecture (Pignatta & Alibrandi, 2022; Zio & Miqueles, 2024) .

Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on cognition lack apparently a unifying framework. This paper formulates a speculative answer attempting to respond to this gap. To postulate on higher-level activation processes from a material perspective, we consider inferential mechanisms informed by symbolic AI modelling techniques, through the simplistic lenses of electronic circuits based on logic gates. We observe that a logic gate view entails a different treatment of implication and negation compared to standard logic and logic programming. Then, by combinatorial exploration, we identify four main forms of dependencies that can be realized by these inferential circuits. Looking at how these forms are generally used in the context of logic programs, we identify eight common inferential patterns, exposing traditionally distinct inferential mechanisms in an unifying framework. Finally, following a probabilistic interpretation of logic programs, we unveil inner functional dependencies. The paper concludes elaborating in what sense, even if our arguments are mostly informed by symbolic means and digital systems infrastructures, our observations may pinpoint to more generally applicable structures.

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification. Bayesian nonparametric methods, especially the \polya tree, offer a robust framework that addresses these issues by accurately capturing function behavior over small intervals. Traditional techniques like Markov chain Monte Carlo (MCMC) face high computational complexity and scalability limitations, hindering the use of Bayesian nonparametric methods in deep learning. To tackle this, we introduce the variational \polya tree (VPT) model, which employs stochastic variational inference to compute posterior distributions. This model provides a flexible, nonparametric Bayesian prior that captures latent densities and works well with stochastic gradient optimization. We also leverage the joint distribution likelihood for a more precise variational posterior approximation than traditional mean-field methods. We evaluate the model performance on both real data and images, and demonstrate its competitiveness with other state-of-the-art deep density estimation methods. We also explore its ability in enhancing interpretability and uncertainty quantification. Code is available at https://github.com/howardchanth/var-polya-tree.

Pre-trained large language models have demonstrated a strong ability to learn from context, known as in-context learning (ICL). Despite a surge of recent applications that leverage such capabilities, it is by no means clear, at least theoretically, how the ICL capabilities arise, and in particular, what is the precise role played by key factors such as pre-training procedure as well as context construction. In this work, we propose a new framework to analyze the ICL performance, for a class of realistic settings, which includes network architectures, data encoding, data generation, and prompt construction process. As a first step, we construct a simple example with a one-layer transformer, and show an interesting result, namely when the pre-train data distribution is different from the query task distribution, a properly constructed context can shift the output distribution towards the query task distribution, in a quantifiable manner, leading to accurate prediction on the query topic. We then extend the findings in the previous step to a more general case, and derive the precise relationship between ICL performance, context length and the KL divergence between pre-train and query task distribution. Finally, we provide experiments to validate our theoretical results.

Machine learning in neurosurgery is limited by challenges in assembling large, high-quality imaging datasets. Synthetic data offers a scalable, privacy-preserving solution. We evaluated the feasibility of generating realistic lateral cervical spine radiographs using a denoising diffusion probabilistic model (DDPM) trained on 4,963 images from the Cervical Spine X-ray Atlas. Model performance was monitored via training/validation loss and Frechet inception distance, and synthetic image quality was assessed in a blinded "clinical Turing test" with six neuroradiologists and two spine-fellowship trained neurosurgeons. Experts reviewed 50 quartets containing one real and three synthetic images, identifying the real image and rating realism on a 4-point Likert scale. Experts correctly identified the real image in 29% of trials (Fleiss' kappa=0.061). Mean realism scores were comparable between real (3.323) and synthetic images (3.228, 3.258, and 3.320; p=0.383, 0.471, 1.000). Nearest-neighbor analysis found no evidence of memorization. We also provide a dataset of 20,063 synthetic radiographs. These results demonstrate that DDPM-generated cervical spine X-rays are statistically indistinguishable in realism and quality from real clinical images, offering a novel approach to creating large-scale neuroimaging datasets for ML applications in landmarking, segmentation, and classification.