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Researcher profile

Kelin Xia

Kelin Xia contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningmath.ATQuantitative MethodsArtificial Intelligence

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Published work

5 published item(s)

preprint2026arXiv

Full-Spectrum Graph Neural Network: Expressive and Scalable

It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNN (FSpecGNN), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering in two perspectives: (1) it lifts the signal from the node domain to the node-pair domain; and (2) it extends the univariate spectral filter over eigenvalues to a bivariate filter over eigenvalue pairs. We show that classical spectral GNNs arise as a diagonal special case of FSpecGNN, and prove that FSpecGNN can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning. Moreover, FSpecGNN admits scalable implementations that avoid explicit node-pair-level computations; combined with a low-rank approximation that reduces full-spectrum convolution to a combination of polynomial spectral filters, it enables learning on large graphs. Empirically, FSpecGNN validates the predicted expressivity and delivers strong performance on heterophilic benchmarks.

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preprint2026arXiv

Topology-Aware Multiscale Mixture of Experts for Efficient Molecular Property Prediction

Many molecular properties depend on 3D geometry, where non-covalent interactions, stereochemical effects, and medium- to long-range forces are determined by spatial distances and angles that cannot be uniquely captured by a 2D bond graph. Yet most 3D molecular graph neural networks still rely on globally fixed neighborhood heuristics, typically defined by distance cutoffs and maximum neighbor limits, to define local message-passing neighborhoods, leading to rigid, data-agnostic interaction budgets. We propose Multiscale Interaction Mixture of Experts (MI-MoE) to adapt interaction modeling across geometric regimes. Our contributions are threefold: (1) we introduce a distance-cutoff expert ensemble that explicitly captures short-, mid-, and long-range interactions without committing to a single cutoff; (2) we design a topological gating encoder that routes inputs to experts using filtration-based descriptors, including persistent homology features, summarizing how connectivity evolves across radii; and (3) we show that MI-MoE is a plug-in module that consistently improves multiple strong 3D molecular backbones across diverse molecular and polymer property prediction benchmark datasets, covering both regression and classification tasks. These results highlight topology-aware multiscale routing as an effective principle for 3D molecular graph learning.

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preprint2020arXiv

Persistent spectral based machine learning (PerSpect ML) for drug design

In this paper, we propose persistent spectral based machine learning (PerSpect ML) models for drug design. Persistent spectral models, including persistent spectral graph, persistent spectral simplicial complex and persistent spectral hypergraph, are proposed based on spectral graph theory, spectral simplicial complex theory and spectral hypergraph theory, respectively. Different from all previous spectral models, a filtration process, as proposed in persistent homology, is introduced to generate multiscale spectral models. More specifically, from the filtration process, a series of nested topological representations, i,e., graphs, simplicial complexes, and hypergraphs, can be systematically generated and their spectral information can be obtained. Persistent spectral variables are defined as the function of spectral variables over the filtration value. Mathematically, persistent multiplicity (of zero eigenvalues) is exactly the persistent Betti number (or Betti curve). We consider 11 persistent spectral variables and use them as the feature for machine learning models in protein-ligand binding affinity prediction. We systematically test our models on three most commonly-used databases, including PDBbind-2007, PDBbind-2013 and PDBbind-2016. Our results, for all these databases, are better than all existing models, as far as we know. This demonstrates the great power of our PerSpect ML in molecular data analysis and drug design.

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preprint2020arXiv

Weighted Fundamental Group

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weighted versions of classical theorems like van Kampen's theorem. In addition, we also investigate the abelianization, lower central series and applications of weighted fundamental groups.

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preprint2019arXiv

Discrete Morse Theory for Weighted Simplicial Complexes

In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key difference in the weighted case is that simplicial collapses do not necessarily preserve weighted homology. We work out some sufficient conditions for collapses to preserve weighted homology, as well as study the effect of elementary removals on weighted homology. An application to sequence analysis is included, where we study the weighted ordered complexes of sequences.

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