GraphCompliance: Aligning Policy and Context Graphs for LLM-Based Regulatory Compliance

Compliance at web scale poses practical challenges: each request may require a regulatory assessment. Regulatory texts (e.g., the General Data Protection Regulation, GDPR) are cross-referential and normative, while runtime contexts are expressed in unstructured natural language. This setting motivates us to align semantic information in unstructured text with the structured, normative elements of regulations. To this end, we introduce GraphCompliance, a framework that represents regulatory texts as a Policy Graph and runtime contexts as a Context Graph, and aligns them. In this formulation, the policy graph encodes normative structure and cross-references, whereas the context graph formalizes events as subject-action-object (SAO) and entity-relation triples. This alignment anchors the reasoning of a judge large language model (LLM) in structured information and helps reduce the burden of regulatory interpretation and event parsing, enabling a focus on the core reasoning step. In experiments on 300 GDPR-derived real-world scenarios spanning five evaluation tasks, GraphCompliance yields 4.1-7.2 percentage points (pp) higher micro-F1 than LLM-only and RAG baselines, with fewer under- and over-predictions, resulting in higher recall and lower false positive rates. Ablation studies indicate contributions from each graph component, suggesting that structured representations and a judge LLM are complementary for normative reasoning.

Efficient Graduated Non-Convexity for Pose Graph Optimization

We propose a novel approach to Graduated Non-Convexity (GNC) and demonstrate its efficacy through its application in robust pose graph optimization, a key component in SLAM backends. Traditional GNC methods often rely on heuristic methods for GNC schedule, updating control parameter {\mu} for escalating the non-convexity. In contrast, our approach leverages the properties of convex functions and convex optimization to identify the boundary points beyond which convexity is no longer guaranteed, thereby eliminating redundant optimization steps in existing methodologies and enhancing both speed and robustness. We show that our method outperforms the state-of-the-art method in terms of speed and accuracy when used for robust back-end pose graph optimization via GNC. Our work builds upon and enhances the open-source riSAM framework. Our implementation can be accessed from: https://github.com/SNU-DLLAB/EGNC-PGO

Adaptive Graduated Non-Convexity for Pose Graph Optimization

We present a novel approach to robust pose graph optimization based on Graduated Non-Convexity (GNC). Unlike traditional GNC-based methods, the proposed approach employs an adaptive shape function using B-spline to optimize the shape of the robust kernel. This aims to reduce GNC iterations, boosting computational speed without compromising accuracy. When integrated with the open-source riSAM algorithm, the method demonstrates enhanced efficiency across diverse datasets. Accompanying open-source code aims to encourage further research in this area. https://github.com/SNU-DLLAB/AGNC-PGO