Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov Chain Monte Carlo (SGMCMC) is one of the most powerful methods for scalable posterior sampling in BNNs, achieving efficiency by combining stochastic gradient descent with second-order Langevin dynamics. However, SGMCMC often suffers from limited sample diversity in practice, which affects uncertainty estimation and model performance. We propose a simple yet effective approach to enhance sample diversity in SGMCMC without the need for tempering or running multiple chains. Our approach reparameterizes the neural network by decomposing each of its weight matrices into a product of matrices, resulting in a sampling trajectory that better explores the target parameter space. This approach produces a more diverse set of samples, allowing faster mixing within the same computational budget. Notably, our sampler achieves these improvements without increasing the inference cost compared to the standard SGMCMC. Extensive experiments on image classification tasks, including OOD robustness, diversity, loss surface analyses, and a comparative study with Hamiltonian Monte Carlo, demonstrate the superiority of the proposed approach.

Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schr\"odinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though na\"ively smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Mat\'ern processes) for which the resulting Smooth Schr\"odinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. The code can be found at https://github.com/WanliHongC/Smooth_SB

Traditional autonomous driving systems often struggle to integrate high-level reasoning with low-level control, resulting in suboptimal and sometimes unsafe driving behaviors. The emergence of Multimodal Large Language Models (MLLMs), which can process both visual and textual data, presents an opportunity to unify perception and reasoning tasks within a single framework. However, effectively embedding precise safety knowledge into MLLMs for autonomous driving remains a significant challenge. To address this, we propose SafeAuto, a novel framework that enhances MLLM-based autonomous driving systems by incorporating both unstructured and structured knowledge. Specifically, we first introduce the Position-Dependent Cross-Entropy (PDCE) loss function, designed to improve the accuracy of low-level control signal predictions when numerical values are represented as text. Second, to ensure safe autonomous driving by explicitly integrating precise safety knowledge into the MLLM, we develop a reasoning component for SafeAuto. This component translates driving safety regulations into first-order logic rules (e.g., "red light => stop") and incorporates these rules into a probabilistic graphical model, such as a Markov Logic Network (MLN). The MLN is trained to verify the predicted next actions using environmental attributes identified by attribute recognition models (e.g., detecting a red light) to form the predicates. Additionally, we construct a Multimodal RAG model that leverages video data, control signals, and environmental attributes to learn more effectively from past similar driving experiences. By integrating PDCE, MLN, and Multimodal RAG, SafeAuto significantly outperforms existing baselines across multiple datasets. This advancement enables more accurate, reliable, and safer autonomous driving systems that learn from experience, obey traffic laws, and perform precise control actions.

IEEE ROBOTICS AND AUTOMA TION LETTERS 1 Dynamically Local-Enhancement Planner for Large-Scale Autonomous Driving Nanshan Deng, Weitao Zhou, Bo Zhang, Junze Wen, Kun Jiang, Zhong Cao, Diange Y ang Abstract --Current autonomous vehicles operate primarily within limited regions, but there is increasing demand for broader applications. However, as models scale, their limited capacity becomes a significant challenge for adapting to novel scenarios. It is increasingly difficult to improve models for new situations using a single monolithic model. T o address this issue, we introduce the concept of dynamically enhancing a basic driving planner with local driving data, without permanently modifying the planner itself. This approach, termed the Dynamically Local-Enhancement (DLE) Planner, aims to improve the scalability of autonomous driving systems without significantly expanding the planner's size. Our approach introduces a position-varying Markov Decision Process formulation coupled with a graph neural network that extracts region-specific driving features from local observation data. The learned features describe the local behavior of the surrounding objects, which is then leveraged to enhance a basic reinforcement learning-based policy. We evaluated our approach in multiple scenarios and compared it with a one-for-all driving model. The results show that our method outperforms the baseline policy in both safety (collision rate) and average reward, while maintaining a lighter scale.

In this article, the two filter formula is re-examined in the setting of partially observed Gauss--Markov models. It is traditionally formulated as a filter running backward in time, where the Gaussian density is parametrized in ``information form''. However, the quantity in the backward recursion is strictly speaking not a distribution, but a likelihood. Taking this observation seriously, a recursion over log-quadratic likelihoods is formulated instead, which obviates the need for ``information'' parametrization. In particular, it greatly simplifies the square-root formulation of the algorithm. Furthermore, formulae are given for producing the forward Markov representation of the a posteriori distribution over paths from the proposed likelihood representation.

Equivariant neural networks play a pivotal role in analyzing datasets with symmetry properties, particularly in complex data structures. However, integrating equivariance with Markov properties presents notable challenges due to the inherent dependencies within such data. Previous research has primarily concentrated on establishing generalization bounds under the assumption of independently and identically distributed data, frequently neglecting the influence of Markov dependencies. In this study, we investigate the impact of Markov properties on generalization performance alongside the role of equivariance within this context. We begin by applying a new McDiarmid's inequality to derive a generalization bound for neural networks trained on Markov datasets, using Rademacher complexity as a central measure of model capacity. Subsequently, we utilize group theory to compute the covering number under equivariant constraints, enabling us to obtain an upper bound on the Rademacher complexity based on this covering number. This bound provides practical insights into selecting low-dimensional irreducible representations, enhancing generalization performance for fixed-width equivariant neural networks.

Reinforcement learning (RL) methods frequently assume that each new observation completely reflects the environment's state, thereby guaranteeing Markovian (one-step) transitions. In practice, partial observability or sensor/actuator noise often invalidates this assumption. This paper proposes a systematic methodology for detecting such violations, combining a partial correlation-based causal discovery process (PCMCI) with a novel Markov Violation score (MVS). The MVS measures multi-step dependencies that emerge when noise or incomplete state information disrupts the Markov property. Classic control tasks (CartPole, Pendulum, Acrobot) serve as examples to illustrate how targeted noise and dimension omissions affect both RL performance and measured Markov consistency. Surprisingly, even substantial observation noise sometimes fails to induce strong multi-lag dependencies in certain domains (e.g., Acrobot). In contrast, dimension-dropping investigations show that excluding some state variables (e.g., angular velocities in CartPole and Pendulum) significantly reduces returns and increases MVS, while removing other dimensions has minimal impact. These findings emphasize the importance of locating and safeguarding the most causally essential dimensions in order to preserve effective single-step learning. By integrating partial correlation tests with RL performance outcomes, the proposed approach precisely identifies when and where the Markov assumption is violated. This framework offers a principled mechanism for developing robust policies, informing representation learning, and addressing partial observability in real-world RL scenarios. All code and experimental logs are accessible for reproducibility (https://github.com/ucsb/markovianess).

Risk-sensitive planning aims to identify policies maximizing some tail-focused metrics in Markov Decision Processes (MDPs). Such an optimization task can be very costly for the most widely used and interpretable metrics such as threshold probabilities or (Conditional) Values at Risk. Indeed, previous work showed that only Entropic Risk Measures (EntRM) can be efficiently optimized through dynamic programming, leaving a hard-to-interpret parameter to choose. We show that the computation of the full set of optimal policies for EntRM across parameter values leads to tight approximations for the metrics of interest. We prove that this optimality front can be computed effectively thanks to a novel structural analysis and smoothness properties of entropic risks. Empirical results demonstrate that our approach achieves strong performance in a variety of decision-making scenarios.

Searching for objects in cluttered environments requires selecting efficient viewpoints and manipulation actions to remove occlusions and reduce uncertainty in object locations, shapes, and categories. In this work, we address the problem of manipulation-enhanced semantic mapping, where a robot has to efficiently identify all objects in a cluttered shelf. Although Partially Observable Markov Decision Processes~(POMDPs) are standard for decision-making under uncertainty, representing unstructured interactive worlds remains challenging in this formalism. To tackle this, we define a POMDP whose belief is summarized by a metric-semantic grid map and propose a novel framework that uses neural networks to perform map-space belief updates to reason efficiently and simultaneously about object geometries, locations, categories, occlusions, and manipulation physics. Further, to enable accurate information gain analysis, the learned belief updates should maintain calibrated estimates of uncertainty. Therefore, we propose Calibrated Neural-Accelerated Belief Updates (CNABUs) to learn a belief propagation model that generalizes to novel scenarios and provides confidence-calibrated predictions for unknown areas. Our experiments show that our novel POMDP planner improves map completeness and accuracy over existing methods in challenging simulations and successfully transfers to real-world cluttered shelves in zero-shot fashion.

The module also clusters features based on geometry and semantics in the map. The hierarchical mapper [B] runs bottom-up, ingesting the RGB and depth images and the odometric path from the robot to build a map. The top level of the map contains the submaps, the middle level the regions, and the bottom level the objects. The local map compsises the loaded submaps. The other submaps are unloaded to save memory (shown here in gray). The planning module [C] consists of a discrete planner that operates on the sparse map and generates a reference path, while the dense Gaussians in the local map are used to find the trajectory to be executed on the robot. Abstract --We address the challenge of task-oriented navigation in unstructured and unknown environments, where robots must incrementally build and reason on rich, metric-semantic maps in real time. Since tasks may require clarification or re-specification, it is necessary for the information in the map to be rich enough to enable generalization across a wide range of tasks. T o effectively execute tasks specified in natural language, we propose a hierarchical representation built on language-embedded Gaussian splatting that enables both sparse semantic planning that lends itself to online operation and dense geometric representation for collision-free navigation. We validate the effectiveness of our method through real-world robot experiments conducted in both cluttered indoor and kilometer-scale outdoor environments, with a competitive ratio of about 60% against privileged baselines. Experiment videos and more details can be found on our project page: https://atlasnav.github.io This, in turn, requires robots to autonomously perceive their surroundings, gather relevant information, and make safe and efficient decisions - capabilities crucial for a variety of open-world tasking approaches over kilometer-scale environments with sparse semantics . To enable these capabilities on-board robots with privacy & compute constraints, we develop a framework to efficiently store and plan on hierarchical metric-semantic maps with visual and inertial sensors only. An overview of our method is shown in Figure 1. A cornerstone of autonomous navigation is the creation of actionable maps that effectively represent the environment and support diverse navigation and task-specific operations. These properties collectively ensure that the proposed map is not only manageable but also capable of supporting large-scale autonomous navigation to complete tasks provided in natural language. To achieve these goals, we propose an agglomerative data structure that is consistent across both geometric and semantic scales built upon 3D Gaussian Splatting [5] (3DGS).