Reliable positioning in GNSS-challenged environments remains a critical challenge for navigation systems. Tightly coupled GNSS/IMU fusion improves robustness but remains vulnerable to non-Gaussian noise and outliers. We present a robust and adaptive factor graph-based fusion framework that directly integrates GNSS pseudorange measurements with IMU preintegration factors and incorporates the Barron loss, a general robust loss function that unifies several m-estimators through a single tunable parameter. By adaptively down weighting unreliable GNSS measurements, our approach improves resilience positioning. The method is implemented in an extended GTSAM framework and evaluated on the UrbanNav dataset. The proposed solution reduces positioning errors by up to 41% relative to standard FGO, and achieves even larger improvements over extended Kalman filter (EKF) baselines in urban canyon environments. These results highlight the benefits of Barron loss in enhancing the resilience of GNSS/IMU-based navigation in urban and signal-compromised environments.

Monocular Simultaneous Localization and Mapping (SLAM) aims to estimate a robot's pose while simultaneously reconstructing an unknown 3D scene using a single camera. While existing monocular SLAM systems generate detailed 3D geometry through dense scene representations, they are computationally expensive due to the need for iterative optimization. To address this challenge, MASt3R-SLAM utilizes learned 3D reconstruction priors, enabling more efficient and accurate estimation of both 3D structures and camera poses. However, MASt3R-SLAM is limited to single-agent operation. In this paper, we extend MASt3R-SLAM to introduce the first multi-agent monocular dense SLAM system. Each agent performs local SLAM using a 3D reconstruction prior, and their individual maps are fused into a globally consistent map through a loop-closure-based map fusion mechanism. Our approach improves computational efficiency compared to state-of-the-art methods, while maintaining similar mapping accuracy when evaluated on real-world datasets.

Wepropose SplitGNN, a graph neural network (GNN)-based approach that learns to solve weighted maximum satisfiabil ity (MaxSAT) problem. SplitGNN incorporates a co-training architecture consisting of supervised message passing mech anism and unsupervised solution boosting layer. A new graph representation called edge-splitting factor graph is proposed to provide more structural information for learning, which is based on spanning tree generation and edge classification. To improve the solutions on challenging and weighted instances, we implement a GPU-accelerated layer applying efficient score calculation and relaxation-based optimization. Exper iments show that SplitGNN achieves 3* faster convergence and better predictions compared with other GNN-based ar chitectures. More notably, SplitGNN successfully finds solu tions that outperform modern heuristic MaxSAT solvers on much larger and harder weighted MaxSAT benchmarks, and demonstrates exceptional generalization abilities on diverse structural instances.

Automated decision-making under uncertainty requires balancing exploitation and exploration. Classical methods treat these separately using heuristics, while Active Inference unifies them through Expected Free Energy (EFE) minimization. However, EFE minimization is computationally expensive, limiting scalability. We build on recent theory recasting EFE minimization as variational inference, formally unifying it with Planning-as-Inference and showing the epistemic drive as a unique entropic contribution. Our main contribution is a novel message-passing scheme for this unified objective, enabling scalable Active Inference in factored-state MDPs and overcoming high-dimensional planning intractability.

We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin bounds known for both standard multi-class and general structured prediction problems. Our guarantees are expressed in terms of a data-dependent complexity measure, \emph{factor graph complexity}, which we show can be estimated from data and bounded in terms of familiar quantities for several commonly used hypothesis sets, and a sparsity measure for features and graphs. Our proof techniques include generalizations of Talagrand's contraction lemma that can be of independent interest. We further extend our theory by leveraging the principle of Voted Risk Minimization (VRM) and show that learning is possible even with complex factor graphs. We present new learning bounds for this advanced setting, which we use to devise two new algorithms, \emph{Voted Conditional Random Field} (VCRF) and \emph{Voted Structured Boosting} (StructBoost). These algorithms can make use of complex features and factor graphs and yet benefit from favorable learning guarantees. We also report the results of experiments with VCRF on several datasets to validate our theory.

We instead rely on weak supervision sources having some structure by virtue of being encoded programmatically.

We present a general theoretical analysis of structured prediction with a series of new results.

These properties are used implicitly in exact inference, but are difficult to harness for approximate inference.