Varsha Narayanan | Searcharxiv

arXiv2026

Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery

Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data. This makes data preparation and model training expensive. We propose Graph Wavelet Compressed Sensing (GWCS), a learning-based framework for offline compression of graph signals by representing them as sparse, interpretable wavelet-domain representations using the spectral graph wavelet transform. The framework combines a nonparametric multilevel importance sampler, which retains high-energy wavelet coefficients within each scale for a given compression ratio, with a scale-aware graph neural network that reconstructs the signal from the sparse coefficients. We evaluate the proposed framework on synthetic approximately band-limited graph signals over random graphs and four PDE simulation datasets over meshes, which include Turbulent Radiative Layer, Viscoelastic Instability, Kolmogorov Flow, and Dynamic Stall. We compare against graph signal sampling methods and graph autoencoder baselines. Results demonstrate that the framework achieves high reconstruction fidelity and substantial data compression compared to existing benchmarks.

cs.LG↗

arXiv2025

RGE-GCN: Recursive Gene Elimination with Graph Convolutional Networks for RNA-seq based Early Cancer Detection

Early detection of cancer plays a key role in improving survival rates, but identifying reliable biomarkers from RNA-seq data is still a major challenge. The data are high-dimensional, and conventional statistical methods often fail to capture the complex relationships between genes. In this study, we introduce RGE-GCN (Recursive Gene Elimination with Graph Convolutional Networks), a framework that combines feature selection and classification in a single pipeline. Our approach builds a graph from gene expression profiles, uses a Graph Convolutional Network to classify cancer versus normal samples, and applies Integrated Gradients to highlight the most informative genes. By recursively removing less relevant genes, the model converges to a compact set of biomarkers that are both interpretable and predictive. We evaluated RGE-GCN on synthetic data as well as real-world RNA-seq cohorts of lung, kidney, and cervical cancers. Across all datasets, the method consistently achieved higher accuracy and F1-scores than standard tools such as DESeq2, edgeR, and limma-voom. Importantly, the selected genes aligned with well-known cancer pathways including PI3K-AKT, MAPK, SUMOylation, and immune regulation. These results suggest that RGE-GCN shows promise as a generalizable approach for RNA-seq based early cancer detection and biomarker discovery (https://rce-gcn.streamlit.app/ ).

cs.LG↗