#01Jul 21, 2026
math.NA
Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^2(Ω)$ A Priori Error Bounds with Application to Mean Escape Time Computation
Nathanael Tepakbong, Jun Fan, Xiang Zhou and 1 more
Motivated by the numerical computation of the Mean Escape Time (MET) $τ:Ω\to\mathbb{R}$ of a stochastic process from a bounded domain $Ω\subseteq\mathbb{R}^d$, we study elliptic Dirichlet boundary value problems (BVPs) using boundary-enforced Physics-Informed Neural Networks (PINNs), in which the Dirichlet condition is imposed exactly by multiplying the network output with a predefined distance-to-boundary approximation $ρ$. Combining approximation-theoretic and statistical-learning arguments for Rectified Quadratic Unit (ReQU) and hyperbolic tangent (tanh) networks, we derive a priori error bounds that make explicit the dependence on $ρ$. In particular, we show that exact boundary enforcement alone is not enough for $H^2(Ω)$ error bounds, and that a sufficient and essentially necessary condition is for $ρ$ to be a smooth distance approximation $\textit{normalized to first order}$, of the kind constructed in arXiv:2104.08426 [math.NA]. We thereby identify this subclass of $\textit{boundary-adapted}$ PINNs as the appropriate neural network ansatz for solving Dirichlet BVPs. Numerical experiments support the theory, showing that appropriate choices of $ρ$ improve accuracy and convergence, while poorly chosen distance functions can substantially degrade the solution. Our proof also yields new VC-dimension bounds for hypothesis spaces of higher-order derivatives of ReQU and tanh networks, together with new approximation bounds for shallow ReQU networks in higher-order Sobolev norms, all of which are of important independent interest.
#02Jul 21, 2026
cs.LG
Conservative Query and Adaptive Regularization for Offline RL Under Uncertainty Estimation
Li-Rong Zhou, Qin-Wen Luo, Sheng-Jun Huang
Offline reinforcement learning (RL) aims to learn an effective policy from a static dataset, but its performance is fundamentally limited by dataset coverage. Action preference queries leverage expert feedback without additional environment interaction, enabling policy improvement during offline training. However, existing methods still face two key challenges: selecting informative preference queries and effectively exploiting the collected feedback. Current approaches typically rely only on the distance between policy actions and dataset actions for query selection, while enforcing fixed constraints that keep the policy close to queried preferences. Such strategies often lead to unstable policy updates and integrate poorly with value regularization. To address these limitations, we propose Conservative Query and Adaptive Regularization under Uncertainty Estimation, a lightweight framework that jointly improves preference querying and preference exploitation. Specifically, we employ a Morse network to estimate the uncertainty of policy actions with respect to the offline dataset. Based on this uncertainty, we introduce a conservative query strategy that selectively queries actions near the dataset to preserve Bellman-update stability, together with an uncertainty-aware adaptive regularization scheme that dynamically adjusts data-level constraints during policy optimization. We integrate our framework with CQL and evaluate it extensively on the D4RL benchmark. Experimental results demonstrate superior or competitive performance across a wide range of tasks.
#03Jul 21, 2026
cs.LG
Toward Auditable Fraud Detection: Combining Graph Features, Model Explanations, and Agentic Case Investigation
Rahil Sharma
Fraud detection systems must scale with rising transaction volume while remaining explainable and reviewable. We study a layered pipeline on the PaySim dataset that combines a gradient-boosted classifier, graph-derived structural features, an autoencoder-based anomaly signal, TreeSHAP explanations, and a bounded LLM investigation agent applied to cases the classifier scores uncertainly. Before any model comparison, we identify and remove a simulator-specific balance shortcut that would otherwise inflate baseline performance. After this correction, neither the graph features nor the anomaly signal improves Average Precision on the full test set. Both, however, rank fraud better within the subset of cases receiving intermediate baseline scores. In a controlled experiment with injected multi-account fraud rings, engineered structural features recover all injected test transactions, while the tabular baseline misses roughly a quarter of them. The investigation agent underperforms direct thresholding of the classifier it relies on, reaching 65.0% accuracy against 71.7% on a balanced 60-case sample, despite having access to model explanations, graph context, and retrieved reference cases. Of the eight decisions the agent changed, six replaced correct classifier outputs with errors, and it produced a coherent written rationale in each case. An exploratory disagreement-based escalation rule flagged two of these agent errors for human review without flagging any correct decision. We conclude that each component of a layered fraud system contributes only under specific conditions, and that a plausible rationale from an investigation agent is not evidence of a better decision.
#04Jul 21, 2026
cs.LG
Staypoint Detection from Noisy Trajectory Data [Experiment Paper]
Lance Kennedy, Hossein Amiri, Yueyang Liu and 9 more
Detecting staypoints from raw trajectory data is fundamental to numerous spatial computing applications. This process transforms raw numeric sequences of geolocations into semantically meaningful locations, such as homes, workplaces, or restaurants. Despite its importance for semantic trajectory analysis, staypoint detection lacks standard benchmarks, and existing algorithms have never been systematically evaluated. This gap persists because no publicly available datasets provide both raw individual trajectories and ground-truth staypoint annotations. This benchmark paper addresses this limitation with two key contributions: (1) we introduce 16 large-scale simulated datasets capturing thousands of agents with annotated staypoints across varying trajectory noise levels, and (2) we evaluate nine staypoint detection algorithms-including both state-of-the-art and novel methods-to analyze their robustness to noise. Our evaluation reveals that existing state-of-the-art algorithms perform poorly under realistic noise conditions. Conversely, our proposed unsupervised methods yield substantial improvements, while supervised approaches drastically outperform existing baselines. While these results are very promising, these datasets and methods are only meant as starting points for future research in staypoint detection.
#05Jul 21, 2026
cs.LG
GUIDED Network-Agnostic Feature Initialization for Spatial Transferability in GNN-based Models
Alessandro Scalese, Santhanakrishnan Narayanan, Constantinos Antoniou
The Traffic Assignment Problem is a fundamental but computationally expensive component of transportation planning. While Graph Neural Networks have emerged as fast, data-driven surrogates, their practical deployment is severely constrained by a spatial generalization gap. Standard models rely on transductive feature initializations that tie travel demand to fixed network topologies, preventing seamless transfer to new urban environments. To overcome this structural limitation, this research proposes a network-agnostic initialization layer, termed Geometrically Unconstrained Inductive Demand EmbeDding (GUIDED). By injecting travel demand as a scalar attribute on auxiliary virtual links rather than as specific node features, this modular framework standardizes the input space regardless of network scale. Extensive experimental evaluation across multiple urban topologies demonstrates that a Heterogeneous Graph Attention Network (HetGAT) model integrated with the proposed GUIDED layer maintains state-of-the-art predictive accuracy on single-network tasks, while demonstrating superior robustness to out-of-distribution demand patterns and maintaining a distinct performance advantage over the baseline even under severe data scarcity. Notably, the proposed feature initialization enables highly parameter-efficient domain adaptation for inter-network transfer learning without artificial input homogenization, establishing a robust foundation for truly inductive models. At the same time, the optimized scatter operations of the initialization layer yield an approximate 50% reduction in training time per epoch compared to the baseline approach. Furthermore, while demonstrated on vehicular traffic, this fundamental abstraction of spatial topology provides a versatile blueprint for generalized origin-destination spatial problems, such as freight logistics and multimodal network optimization.