arXiv:2603.26738v2 Announce Type: replace-cross Abstract: While automated sleep staging has achieved expert-level accuracy, its clinical adoption is hindered by a lack of auditable reasoning. We introduce SleepVLM, a rule-grounded vision-language model (VLM) designed to stage sleep from multi-channel polysomnography (PSG) waveform images while generating clinician-readable rationales based on American Academy of Sleep Medicine (AASM) scoring criteria. Utilizing waveform-perceptual pre-training and rule-grounded supervised fine-tuning, SleepVLM achieved Cohen's kappa scores of 0.767 on an held out test set (MASS-SS1) and 0.743 on an external cohort (ZUAMHCS), matching state-of-the-art performance. Expert evaluations further validated the quality of the model's reasoning, with mean scores exceeding 4.0/5.0 for factual accuracy, evidence comprehensiveness, and logical coherence. By coupling competitive performance with transparent, rule-based explanations, SleepVLM may improve the trustworthiness and auditability of automated sleep staging in clinical workflows. To facilitate further research in interpretable sleep medicine, we release MASS-EX, a novel expert-annotated dataset.

arXiv:2603.22380v1 Announce Type: cross Abstract: Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and limited by sparse sampling, which poses significant challenges to existing approaches based on numerical differentiation or integral formulations. In this work, we propose a Symbolic Graph Network (SGN) framework for PDE discovery under noisy and sparse conditions. Instead of relying on local differential approximations, SGN leverages graph message passing to model spatial interactions, providing a non-local representation that is less sensitive to high frequency noise. Based on this representation, the learned latent features are further processed by a symbolic regression module to extract interpretable mathematical expressions. We evaluate the proposed method on several benchmark systems, including the wave equation, convection-diffusion equation, and incompressible Navier-Stokes equations. Experimental results show that SGN can recover meaningful governing relations or solution forms under varying noise levels, and demonstrates improved robustness compared to baseline methods in sparse and noisy settings. These results suggest that combining graph-based representations with symbolic regression provides a viable direction for robust data-driven discovery of physical laws from imperfect observations. The code is available at https://github.com/CXY0112/SGN