Dai Shi

Dai Shi, Yi Guo, Zhiqi Shao et al.

Graph neural network (GNN) has been demonstrated powerful in modeling graph-structured data. However, despite many successful cases of applying GNNs to various graph classification and prediction tasks, whether the graph geometrical information has been fully exploited to enhance the learning performance of GNNs is not yet well understood. This paper introduces a new approach to enhance GNN by discrete graph Ricci curvature. Specifically, the graph Ricci curvature defined on the edges of a graph measures how difficult the information transits on one edge from one node to another based on their neighborhoods. Motivated by the geometric analogy of Ricci curvature in the graph setting, we prove that by inserting the curvature information with different carefully designed transformation function $ζ$, several known computational issues in GNN such as over-smoothing can be alleviated in our proposed model. Furthermore, we verified that edges with very positive Ricci curvature (i.e., $κ_{i,j} \approx 1$) are preferred to be dropped to enhance model's adaption to heterophily graph and one curvature based graph edge drop algorithm is proposed. Comprehensive experiments show that our curvature-based GNN model outperforms the state-of-the-art baselines in both homophily and heterophily graph datasets, indicating the effectiveness of involving graph geometric information in GNNs.

Kuan Yan, Yue Zeng, Dai Shi et al.

Age-related macular degeneration (AMD) is a major cause of blindness in older adults, severely affecting vision and quality of life. Despite advances in understanding AMD, the molecular factors driving the severity of subretinal scarring (fibrosis) remain elusive, hampering the development of effective therapies. This study introduces a machine learning-based framework to predict key genes that are strongly correlated with lesion severity and to identify potential therapeutic targets to prevent subretinal fibrosis in AMD. Using an original RNA sequencing (RNA-seq) dataset from the diseased retinas of JR5558 mice, we developed a novel and specific feature engineering technique, including pathway-based dimensionality reduction and gene-based feature expansion, to enhance prediction accuracy. Two iterative experiments were conducted by leveraging Ridge and ElasticNet regression models to assess biological relevance and gene impact. The results highlight the biological significance of several key genes and demonstrate the framework's effectiveness in identifying novel therapeutic targets. The key findings provide valuable insights for advancing drug discovery efforts and improving treatment strategies for AMD, with the potential to enhance patient outcomes by targeting the underlying genetic mechanisms of subretinal lesion development.

Dai Shi, Kuan Yan, Lequan Lin et al.

Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by developing a biologically informed graph-forming method to efficiently construct pathway graphs for subjects from our newly curated JR5558 mouse transcriptomics dataset. We then develop Graph-level Pseudotime Analysis (GPA) to infer graph-level trajectories that reveal how disease progresses at the population level, rather than in individual subjects. Based on the trajectories estimated by GPA, we identify the most sensitive pathways that drive disease stage transitions. In addition, we measure changes in pathway features using neural stochastic differential equations (SDEs), which enables us to formally define and compute pathway stability and disease bifurcation points (points of no return), two fundamental problems in disease progression research. We further extend our theory to the case when pathways can interact with each other, enabling a more comprehensive and multi-faceted characterization of disease phenotypes. The comprehensive experimental results demonstrate the effectiveness of our framework in reconstructing the dynamics of the pathway, identifying critical transitions, and providing novel insights into the mechanistic understanding of disease evolution.

Luke Thompson, Davy Guan, Dai Shi et al.

Molecular dynamics (MD) simulations underpin modern computational drug dis- covery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need to repeatedly solve quantum mechanical forces, enabling significant speedups over conventional pipelines. Yet many such methods typically enforce strict equivariance and rely on sequential rollouts, thus limiting their flexibility and simulation efficiency. They are also com- monly single-task, trained on individual molecules and fixed timeframes, which restricts generalization to unseen compounds and extended timesteps. To address these issues, we propose Atomistic Transformer Operator for Molecules (ATOM), a pretrained transformer neural operator for multitask molecular dynamics. ATOM adopts a quasi-equivariant design that requires no explicit molecular graph and employs a temporal attention mechanism, allowing for the accurate parallel decod- ing of multiple future states. To support operator pretraining across chemicals and timescales, we curate TG80, a large, diverse, and numerically stable MD dataset with over 2.5 million femtoseconds of trajectories across 80 compounds. ATOM achieves state-of-the-art performance on established single-task benchmarks, such as MD17, RMD17 and MD22. After multitask pretraining on TG80, ATOM shows exceptional zero-shot generalization to unseen molecules across varying time hori- zons. We believe ATOM represents a significant step toward accurate, efficient, and transferable molecular dynamics models

Lequan Lin, Dai Shi, Andi Han et al.

Traffic forecasting, a crucial application of spatio-temporal graph (STG) learning, has traditionally relied on deterministic models for accurate point estimations. Yet, these models fall short of quantifying future uncertainties. Recently, many probabilistic methods, especially variants of diffusion models, have been proposed to fill this gap. However, existing diffusion methods typically deal with individual sensors separately when generating future time series, resulting in limited usage of spatial information in the probabilistic learning process. In this work, we propose SpecSTG, a novel spectral diffusion framework, to better leverage spatial dependencies and systematic patterns inherent in traffic data. More specifically, our method generates the Fourier representation of future time series, transforming the learning process into the spectral domain enriched with spatial information. Additionally, our approach incorporates a fast spectral graph convolution designed for Fourier input, alleviating the computational burden associated with existing models. Compared with state-of-the-arts, SpecSTG achieves up to 8% improvements on point estimations and up to 0.78% improvements on quantifying future uncertainties. Furthermore, SpecSTG's training and validation speed is 3.33X of the most efficient existing diffusion method for STG forecasting. The source code for SpecSTG is available at https://anonymous.4open.science/r/SpecSTG.

Dai Shi, Andi Han, Yi Guo et al.

Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroinformatics. However, the understanding of whether DR and ManL models can generate valid learning results remains unclear. In this work, we investigate the validity of learning results of some widely used DR and ManL methods through the chart mapping function of a manifold. We identify a fundamental problem of these methods: the mapping functions induced by these methods violate the basic settings of manifolds, and hence they are not learning manifold in the mathematical sense. To address this problem, we provide a provably correct algorithm called fixed points Laplacian mapping (FPLM), that has the geometric guarantee to find a valid manifold representation (up to a homeomorphism). Combining one additional condition(orientation preserving), we discuss a sufficient condition for an algorithm to be bijective for any d-simplex decomposition result on a d-manifold. However, constructing such a mapping function and its computational method satisfying these conditions is still an open problem in mathematics.