Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.

We propose Network Automatic Relevance Determination (NARD), an extension of ARD for linearly probabilistic models, to simultaneously model sparse relationships between inputs $X \in \mathbb R^{d \times N}$ and outputs $Y \in \mathbb R^{m \times N}$, while capturing the correlation structure among the $Y$. NARD employs a matrix normal prior which contains a sparsity-inducing parameter to identify and discard irrelevant features, thereby promoting sparsity in the model. Algorithmically, it iteratively updates both the precision matrix and the relationship between $Y$ and the refined inputs. To mitigate the computational inefficiencies of the $\mathcal O(m^3 + d^3)$ cost per iteration, we introduce Sequential NARD, which evaluates features sequentially, and a Surrogate Function Method, leveraging an efficient approximation of the marginal likelihood and simplifying the calculation of determinant and inverse of an intermediate matrix. Combining the Sequential update with the Surrogate Function method further reduces computational costs. The computational complexity per iteration for these three methods is reduced to $\mathcal O(m^3+p^3)$, $\mathcal O(m^3 + d^2)$, $\mathcal O(m^3+p^2)$, respectively, where $p \ll d$ is the final number of features in the model. Our methods demonstrate significant improvements in computational efficiency with comparable performance on both synthetic and real-world datasets.

Causal discovery (CD) plays a pivotal role in understanding the mechanisms underlying complex systems. While recent algorithms can detect spurious associations and latent confounding, many struggle to recover fairness-relevant pathways in realistic, noisy settings. Large Language Models (LLMs), with their access to broad semantic knowledge, offer a promising complement to statistical CD approaches, particularly in domains where metadata provides meaningful relational cues. Ensuring fairness in machine learning requires understanding how sensitive attributes causally influence outcomes, yet CD methods often introduce spurious or biased pathways. We propose a hybrid LLM-based framework for CD that extends a breadth-first search (BFS) strategy with active learning and dynamic scoring. Variable pairs are prioritized for LLM-based querying using a composite score based on mutual information, partial correlation, and LLM confidence, improving discovery efficiency and robustness. To evaluate fairness sensitivity, we construct a semi-synthetic benchmark from the UCI Adult dataset, embedding a domain-informed causal graph with injected noise, label corruption, and latent confounding. We assess how well CD methods recover both global structure and fairness-critical paths. Our results show that LLM-guided methods, including the proposed method, demonstrate competitive or superior performance in recovering such pathways under noisy conditions. We highlight when dynamic scoring and active querying are most beneficial and discuss implications for bias auditing in real-world datasets.

-- This paper investigates how an autonomous agent can transmit information through its motion in an adversarial setting. We consider scenarios where an agent must reach its goal while deceiving an intelligent observer about its destination. We model this interaction as a dynamic Bayesian game between a mobile Attacker with a privately known goal and a Defender who infers the Attacker's intent to allocate defensive resources effectively. We use Perfect Bayesian Nash Equilibrium (PBNE) as our solution concept and propose a computationally efficient approach to find it. In the resulting equilibrium, the Defender employs a simple Markovian strategy, while the Attacker strategically balances deception and goal efficiency by stochastically mixing shortest and non-shortest paths to manipulate the Defender's beliefs. Numerical experiments demonstrate the advantages of our PBNE-based strategies over existing methods based on one-sided optimization.

LPMLN is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LPMLN and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LPMLN into programs with weak constraints and a translation of P-log into LPMLN, which complement the existing translations in the opposite directions. The first translation allows us to compute the most probable stable models (i.e., MAP estimates) of LPMLN programs using standard ASP solvers. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl's Causal Models, that are shown to be translatable into LPMLN. The second translation tells us how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers and MLN solvers.

Scaling has been a major driver of recent advancements in deep learning. Numerous empirical studies have found that scaling laws often follow the power-law and proposed several variants of power-law functions to predict the scaling behavior at larger scales. However, existing methods mostly rely on point estimation and do not quantify uncertainty, which is crucial for real-world applications involving decision-making problems such as determining the expected performance improvements achievable by investing additional computational resources. In this work, we explore a Bayesian framework based on Prior-data Fitted Networks (PFNs) for neural scaling law extrapolation. Specifically, we design a prior distribution that enables the sampling of infinitely many synthetic functions resembling real-world neural scaling laws, allowing our PFN to meta-learn the extrapolation. We validate the effectiveness of our approach on real-world neural scaling laws, comparing it against both the existing point estimation methods and Bayesian approaches. Our method demonstrates superior performance, particularly in data-limited scenarios such as Bayesian active learning, underscoring its potential for reliable, uncertainty-aware extrapolation in practical applications.

Reinforcement learning (RL) is playing an increasingly important role in fields such as robotic control and autonomous driving. However, the gap between simulation and the real environment remains a major obstacle to the practical deployment of RL. Agents trained in simulators often struggle to maintain performance when transferred to real-world physical environments. In this paper, we propose a latent space based approach to analyze the impact of simulation on real-world policy improvement in model-based settings. As a natural extension of model-based methods, our approach enables an intuitive observation of the challenges faced by model-based methods in sim-to-real transfer. Experiments conducted in the MuJoCo environment evaluate the performance of our method in both measuring and mitigating the sim-to-real gap. The experiments also highlight the various challenges that remain in overcoming the sim-to-real gap, especially for model-based methods.

Intelligent Transportation Systems (ITSs) have emerged as a promising solution towards ameliorating urban traffic congestion, with Traffic Signal Control (TSC) identified as a critical component. Although Multi-Agent Reinforcement Learning (MARL) algorithms have shown potential in optimizing TSC through real-time decision-making, their scalability and effectiveness often suffer from large-scale and complex environments. Typically, these limitations primarily stem from a fundamental mismatch between the exponential growth of the state space driven by the environmental heterogeneities and the limited modeling capacity of current solutions. To address these issues, this paper introduces a novel MARL framework that integrates Dynamic Graph Neural Networks (DGNNs) and Topological Data Analysis (TDA), aiming to enhance the expressiveness of environmental representations and improve agent coordination. Furthermore, inspired by the Mixture of Experts (MoE) architecture in Large Language Models (LLMs), a topology-assisted spatial pattern disentangling (TSD)-enhanced MoE is proposed, which leverages topological signatures to decouple graph features for specialized processing, thus improving the model's ability to characterize dynamic and heterogeneous local observations. The TSD module is also integrated into the policy and value networks of the Multi-agent Proximal Policy Optimization (MAPPO) algorithm, further improving decision-making efficiency and robustness. Extensive experiments conducted on real-world traffic scenarios, together with comprehensive theoretical analysis, validate the superior performance of the proposed framework, highlighting the model's scalability and effectiveness in addressing the complexities of large-scale TSC tasks.

The identification of channel scenarios in wireless systems plays a crucial role in channel modeling, radio fingerprint positioning, and transceiver design. Traditional methods to classify channel scenarios are based on typical statistical characteristics of channels, such as K-factor, path loss, delay spread, etc. However, statistic-based channel identification methods cannot accurately differentiate implicit features induced by dynamic scatterers, thus performing very poorly in identifying similar channel scenarios. In this paper, we propose a novel channel scenario identification method, formulating the identification task as a maximum a posteriori (MAP) estimation. Furthermore, the MAP estimation is reformulated by a maximum likelihood estimation (MLE), which is then approximated and solved by the conditional generative diffusion model. Specifically, we leverage a transformer network to capture hidden channel features in multiple latent noise spaces within the reverse process of the conditional generative diffusion model. These detailed features, which directly affect likelihood functions in MLE, enable highly accurate scenario identification. Experimental results show that the proposed method outperforms traditional methods, including convolutional neural networks (CNNs), back-propagation neural networks (BPNNs), and random forest-based classifiers, improving the identification accuracy by more than 10%.

Deterministic Markov Decision Processes (DMDPs) are a mathematical framework for decision-making where the outcomes and future possible actions are deterministically determined by the current action taken. DMDPs can be viewed as a finite directed weighted graph, where in each step, the controller chooses an outgoing edge. An objective is a measurable function on runs (or infinite trajectories) of the DMDP, and the value for an objective is the maximal cumulative reward (or weight) that the controller can guarantee. We consider the classical mean-payoff (aka limit-average) objective, which is a basic and fundamental objective. Howard's policy iteration algorithm is a popular method for solving DMDPs with mean-payoff objectives. Although Howard's algorithm performs well in practice, as experimental studies suggested, the best known upper bound is exponential and the current known lower bound is as follows: For the input size $I$, the algorithm requires $\tildeΩ(\sqrt{I})$ iterations, where $\tildeΩ$ hides the poly-logarithmic factors, i.e., the current lower bound on iterations is sub-linear with respect to the input size. Our main result is an improved lower bound for this fundamental algorithm where we show that for the input size $I$, the algorithm requires $\tildeΩ(I)$ iterations.