Barycentric Weak Inner-Product Gromov-Wasserstein

Gromov-Wasserstein (GW) compares distributions through relations within each space. This pointwise comparison can be too sensitive in one-to-many settings, where several target outcomes refine one source state and their mean carries the geometry of interest. We introduce a weak GW framework that compares source relations with relations between the target conditional laws induced by a coupling. For inner-product relations, we retain the conditional means $m_π(x)=\mathbb{E}_π[Y\mid X=x]$. The resulting barycentric weak inner-product GW (wIGW) satisfies $\mathrm{wIGW}_{\mathrm{bar}}^2(μ,ν)=\inf_{η\preceq_{\mathrm{cx}}ν}\mathrm{IGW}^2(μ,η)$. Here $η\preceq_{\mathrm{cx}}ν$ means that $ν$ is a mean-preserving spread of $η$. Thus wIGW searches for an intermediate target geometry that can be refined into the prescribed target law without changing conditional means. Under finite second moments, minimizers exist and martingale gluing recovers an optimal coupling. With ridge regularization, moment duality gives an $A$-$B$ min-max problem whose inner step is weak optimal transport with a quadratic cost parameterized by $A$ and $B$; the outer problem optimizes these matrices. For finitely supported measures, we give an iterative algorithm. Under a quantitative ridge condition, the reduced problem is convex--concave, and the projected outer iteration satisfies an explicit contraction bound for inexact inner solves. Point cloud and graph feature refinement experiments illustrate how mean-preserving target refinements can have zero cost. A paired peripheral blood mononuclear cell (PBMC) multiome study evaluates atlas based cell type transfer through RNA/ATAC alignment in cell to cell and prototype to cell settings, with the prototype to cell setting representing the one-to-many case.

GenEx: A Graph-Based Representational Paradigm for SARS-CoV-2 Variant Detection via Codon Co-occurrence Networks

Genomic analysis on viruses such as SARS-CoV-2 variants: Beta, Gamma, Delta, and Omicron is heavily dominated by classical bioinformatics methods, including Sequence Alignment, Phylogenetic Analysis, and Mutation Frequency Statistics. These approaches use pairwise codon or nucleotide distance matrices to analyze gene sequences, treating them as linear strings rather than capturing their complex contextual interdependencies. We proposed GenEx, a pipeline that converts raw gene sequences into codon co-occurrence graphs and extracts more than 25 graph features. Our two most prominent techniques for graph generation and feature extraction are MSCG (Multi-Scale Codon Co-occurrence Graph) and LAPCG (Linear-time Adjacency PMI Codon Graph). Using these algorithms, we treated codon sequences as structured symbolic vocabularies interpretable to codon co-occurrence graph analysis, a representational paradigm borrowed from computational linguistics. Another major contribution includes implementing a spectral graph feature extraction using Singular Value Decomposition (SVD), using the squared singular value ($σ^2$) instead of the traditionally used eigenvalue, which helped us to amplify the separation between dominant and subdominant spectral components, thereby enhancing inter-class separability in downstream classification. And to further demonstrate that our method works, we trained 23 benchmarked ML models against the latest SARS-CoV-2 variants, achieving remarkable results in detecting all SARS-CoV-2 variants.

LLM-Guided Graph Generation for Structure-Based Local Improvement Methods

Large neighborhood search normally selects a random subset of decision variables for iterative optimization. For efficiently solving different problems, researchers tend to design variable selection strategies by taking into account structural features from different domains. In this paper, we build an automatic pipeline that is problem-agnostic to all problems in the MiniZinc format. By prompting an LLM with our semantic guidelines, we guide the LLM to produce a graph generator that maps any instance of a problem type to a uniform weighted graph, where nodes represent decision variables and edges represent constraint relationships. These problem-agnostic graphs guide our structure-based local improvement framework (SLIM) in variable selection. Meanwhile, the weighted graph enables all problem instances to share the same generic graph representation, from which the same graph features can be extracted and used for configuration selection. We evaluated our pipeline on instances across 20 MiniZinc competition problems, finding that algorithm selection achieves a 39.5% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%). Configuration and feature ablation boost the performance further to 44.0%, demonstrating that LLM-based semantic generation enables effective automated structure extraction and feature extraction for constraint optimization.

Toward Auditable Fraud Detection: Combining Graph Features, Model Explanations, and Agentic Case Investigation

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.