5 papers
Lipschitz Bounds for Persistent Laplacian Eigenvalues under One-Simplex Insertions
Le Vu Anh, Mehmet Dik, Nguyen Viet Anh
Persistent Laplacians are matrix operators that track how the shape and structure of data transform across scales and are popularly adopted in biology, physics, and machine learnin…
MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing
Le Vu Anh, Nguyen Viet Anh, Mehmet Dik +1
Real-time mesh smoothing at scale remains a formidable challenge: classical Ricci-flow solvers demand costly global updates, while greedy heuristics suffer from slow convergence or…
RePCS: Diagnosing Data Memorization in LLM-Powered Retrieval-Augmented Generation
Le Vu Anh, Nguyen Viet Anh, Mehmet Dik +1
Retrieval-augmented generation (RAG) has become a common strategy for updating large language model (LLM) responses with current, external information. However, models may still re…
Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
Le Vu Anh, Mehmet Dik, Nguyen Viet Anh
Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted oper…
RN-F: A Novel Approach for Mitigating Contaminated Data in Large Language Models
Le Vu Anh, Dinh Duc Nha Nguyen, Phi Long Nguyen
Large Language Models (LLMs) have become foundational in modern artificial intelligence, powering a wide range of applications from code generation and virtual assistants to scient…