Lam Nguyen

Michael V. Klibanov, Aleksandr E. Kolesov, Anders Sullivan et al.

A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function", which is a complement of a certain truncated integral with respect to the wave number. Globally strictly convex cost functional is constructed with the Carleman Weight Function. Global convergence of the gradient projection method to the correct solution is proved. Numerical tests are conducted for both computationally simulated and experimental data.

Michael V. Klibanov, Aleksandr E. Kolesov, Lam Nguyen et al.

A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other words, this is the function, which is present in the Carleman estimate for the undelying differential operator. The presence of the CWF makes this functional strictly convex on any a priori chosen ball with the center at $\left\{ 0\right\} $ in an appropriate Hilbert space. Convergence of the gradient minimization method to the exact solution starting from any point of that ball is proven. Computational results for both computationally simulated and experimental data show a good accuracy of this method.

Zi-Han Wang, Lam Nguyen, Zhengyang Zhao et al.

The saturation of high-quality pre-training data has shifted research focus toward evolutionary systems capable of continuously generating novel artifacts, leading to the success of AlphaEvolve. However, the progress of such systems is hindered by the lack of rigorous, quantitative evaluation. To tackle this challenge, we introduce CreativeBench, a benchmark for evaluating machine creativity in code generation, grounded in a classical cognitive framework. Comprising two subsets -- CreativeBench-Combo and CreativeBench-Explore -- the benchmark targets combinatorial and exploratory creativity through an automated pipeline utilizing reverse engineering and self-play. By leveraging executable code, CreativeBench objectively distinguishes creativity from hallucination via a unified metric defined as the product of quality and novelty. Our analysis of state-of-the-art models reveals distinct behaviors: (1) scaling significantly improves combinatorial creativity but yields diminishing returns for exploration; (2) larger models exhibit ``convergence-by-scaling,'' becoming more correct but less divergent; and (3) reasoning capabilities primarily benefit constrained exploration rather than combination. Finally, we propose EvoRePE, a plug-and-play inference-time steering strategy that internalizes evolutionary search patterns to consistently enhance machine creativity.

Yifeng Huang, Duc Duy Nguyen, Lam Nguyen et al.

This paper addresses the task of counting human actions of interest using sensor data from wearable devices. We propose a novel exemplar-based framework, allowing users to provide exemplars of the actions they want to count by vocalizing predefined sounds ''one'', ''two'', and ''three''. Our method first localizes temporal positions of these utterances from the audio sequence. These positions serve as the basis for identifying exemplars representing the action class of interest. A similarity map is then computed between the exemplars and the entire sensor data sequence, which is further fed into a density estimation module to generate a sequence of estimated density values. Summing these density values provides the final count. To develop and evaluate our approach, we introduce a diverse and realistic dataset consisting of real-world data from 37 subjects and 50 action categories, encompassing both sensor and audio data. The experiments on this dataset demonstrate the viability of the proposed method in counting instances of actions from new classes and subjects that were not part of the training data. On average, the discrepancy between the predicted count and the ground truth value is 7.47, significantly lower than the errors of the frequency-based and transformer-based methods. Our project, code and dataset can be found at https://github.com/cvlab-stonybrook/ExRAC.

Anthony Baez, Wang Zhang, Ziwen Ma et al.

We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations (PDEs) enables necessary flexibility during training, it also permits the discovered solution to violate physical laws. To address this, we introduce a projection method that guarantees the conservation of the linear and quadratic integrals, both separately and jointly. We derived the projection formulae by solving constrained non-linear optimization problems and found that our PINN modified with the projection, which we call PINN-Proj, reduced the error in the conservation of these quantities by three to four orders of magnitude compared to the soft constraint and marginally reduced the PDE solution error. We also found evidence that the projection improved convergence through improving the conditioning of the loss landscape. Our method holds promise as a general framework to guarantee the conservation of any integral quantity in a PINN if a tractable solution exists.

Tung Vu, Lam Nguyen, Quynh Dao

The proliferation of Large Language Models (LLMs) in real-world applications poses unprecedented risks of generating harmful, biased, or misleading information to vulnerable populations including LGBTQ+ individuals, single parents, and marginalized communities. While existing safety approaches rely on post-hoc filtering or generic alignment techniques, they fail to proactively prevent harmful outputs at the generation source. This paper introduces PromptGuard, a novel modular prompting framework with our breakthrough contribution: VulnGuard Prompt, a hybrid technique that prevents harmful information generation using real-world data-driven contrastive learning. VulnGuard integrates few-shot examples from curated GitHub repositories, ethical chain-of-thought reasoning, and adaptive role-prompting to create population-specific protective barriers. Our framework employs theoretical multi-objective optimization with formal proofs demonstrating 25-30% analytical harm reduction through entropy bounds and Pareto optimality. PromptGuard orchestrates six core modules: Input Classification, VulnGuard Prompting, Ethical Principles Integration, External Tool Interaction, Output Validation, and User-System Interaction, creating an intelligent expert system for real-time harm prevention. We provide comprehensive mathematical formalization including convergence proofs, vulnerability analysis using information theory, and theoretical validation framework using GitHub-sourced datasets, establishing mathematical foundations for systematic empirical research.

Lam Nguyen, Erika Barcelos, Roger French et al.

Ontology Matching (OM) is a cornerstone task of semantic interoperability, yet existing systems often rely on handcrafted rules or specialized models with limited adaptability. We present KROMA, a novel OM framework that harnesses Large Language Models (LLMs) within a Retrieval-Augmented Generation (RAG) pipeline to dynamically enrich the semantic context of OM tasks with structural, lexical, and definitional knowledge. To optimize both performance and efficiency, KROMA integrates a bisimilarity-based concept matching and a lightweight ontology refinement step, which prune candidate concepts and substantially reduce the communication overhead from invoking LLMs. Through experiments on multiple benchmark datasets, we show that integrating knowledge retrieval with context-augmented LLMs significantly enhances ontology matching, outperforming both classic OM systems and cutting-edge LLM-based approaches while keeping communication overhead comparable. Our study highlights the feasibility and benefit of the proposed optimization techniques (targeted knowledge retrieval, prompt enrichment, and ontology refinement) for ontology matching at scale.

Dung N. Tran, Trac D. Tran, Lam Nguyen

Ultra-wideband (UWB) radar systems nowadays typical operate in the low frequency spectrum to achieve penetration capability. However, this spectrum is also shared by many others communication systems, which causes missing information in the frequency bands. To recover this missing spectral information, we propose a generative adversarial network, called SARGAN, that learns the relationship between original and missing band signals by observing these training pairs in a clever way. Initial results shows that this approach is promising in tackling this challenging missing band problem.

Tiep Vu, Lam Nguyen, Vishal Monga

Using low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture radar (SAR) technology for detecting buried and obscured targets, e.g. bomb or mine, has been successfully demonstrated recently. Despite promising recent progress, a significant open challenge is to distinguish obscured targets from other (natural and manmade) clutter sources in the scene. The problem becomes exacerbated in the presence of noisy responses from rough ground surfaces. In this paper, we present three novel sparsity-driven techniques, which not only exploit the subtle features of raw captured data but also take advantage of the polarization diversity and the aspect angle dependence information from multi-channel SAR data. First, the traditional sparse representation-based classification (SRC) is generalized to exploit shared information of classes and various sparsity structures of tensor coefficients for multi-channel data. Corresponding tensor dictionary learning models are consequently proposed to enhance classification accuracy. Lastly, a new tensor sparsity model is proposed to model responses from multiple consecutive looks of objects, which is a unique characteristic of the dataset we consider. Extensive experimental results on a high-fidelity electromagnetic simulated dataset and radar data collected from the U.S. Army Research Laboratory side-looking SAR demonstrate the advantages of proposed tensor sparsity models.

Tiep Vu, Lam Nguyen, Tiantong Guo et al.

Classifying buried and obscured targets of interest from other natural and manmade clutter objects in the scene is an important problem for the U.S. Army. Targets of interest are often represented by signals captured using low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture radar (SAR) technology. This technology has been used in various applications, including ground penetration and sensing-through-the-wall. However, the technology still faces a significant issues regarding low-resolution SAR imagery in this particular frequency band, low radar cross sections (RCS), small objects compared to radar signal wavelengths, and heavy interference. The classification problem has been firstly, and partially, addressed by sparse representation-based classification (SRC) method which can extract noise from signals and exploit the cross-channel information. Despite providing potential results, SRC-related methods have drawbacks in representing nonlinear relations and dealing with larger training sets. In this paper, we propose a Simultaneous Decomposition and Classification Network (SDCN) to alleviate noise inferences and enhance classification accuracy. The network contains two jointly trained sub-networks: the decomposition sub-network handles denoising, while the classification sub-network discriminates targets from confusers. Experimental results show significant improvements over a network without decomposition and SRC-related methods.