Selected work

Representative Papers

Improving Function Space Flow Matching with Kernel Optimal Transport

Sep 29, 2026

This study addresses the inefficient transport paths and lack of geometric structure caused by independent endpoint pairing in generative models over function spaces. To this end, we propose Kernel Flow Matching, which replaces random pairing with entropic optimal transport under the Hilbert-Sinkhorn divergence. By introducing a kernel-induced cost, the method enables infinite-dimensional optimal transport to improve function distribution learning. Theoretically, we establish target boundedness and discretization invariance while isolating irreducible error terms. Empirically, our approach significantly outperforms baselines such as FFM on time series forecasting and PDE benchmarks, and its effectiveness is further validated in modeling turbulent Navier-Stokes equations.

0 citationsRead paper

A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion

Sep 28, 2026

This study addresses the limitation of existing graph neural networks (GNNs) that require separate models for calibration, out-of-distribution (OOD) detection, and robustness tasks. To this end, we propose DSS-GNN, a unified framework that leverages dual spectral stochastic expansion—integrating graph Fourier filtering with orthogonal polynomial chaos expansion—to characterize uncertainty comprehensively. Coupled with energy-based scoring, this approach enables a single model to jointly perform prediction, calibration, and OOD detection within a hybrid deployment setting. Extensive experiments demonstrate that DSS-GNN achieves the lowest Brier scores across 14 benchmarks and attains state-of-the-art shifted accuracy on 7 GOOD benchmarks. These results confirm that the proposed framework effectively resolves the multi-model fragmentation problem in GNN uncertainty quantification, offering a cohesive and highly performant solution for reliable graph representation learning.

0 citationsRead paper

Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations

Jun 07, 2025

Graph Neural Networks (GNNs) struggle to reliably quantify predictive uncertainty under distributional shift, primarily because conventional approaches fail to jointly model the dual stochasticity inherent in graph structure and label distribution. Method: We establish, for the first time, a theoretical analogy between stochastic partial differential equation (SPDE)-driven Matérn Gaussian processes and GNN message passing. Based on this, we propose SPDE-GNN: a framework that employs SPDEs as the kernel for structural-aware stochastic message passing; incorporates Matérn priors for joint spatiotemporal uncertainty modeling; and enables tunable smoothness of the covariance kernel. Contribution/Results: Coupled with structural-aware noise injection and an out-of-distribution (OOD) evaluation framework, SPDE-GNN achieves significant improvements over state-of-the-art methods across diverse graph OOD detection tasks—particularly maintaining high robustness and calibration accuracy even when label informativeness varies substantially.

0 citationsRead paper

When to retrain a machine learning model

May 20, 2025

In real-world deployment, deciding when to retrain machine learning models faces three key challenges: sparse observational samples, unknown characteristics of data distribution shifts, and the difficulty of balancing retraining cost against performance degradation. This paper proposes the first retraining decision framework grounded in performance evolution prediction and uncertainty modeling. It explicitly jointly models performance decay trends, predictive uncertainty bounds, and temporal performance dynamics, and incorporates a cost-aware decision mechanism. Departing from conventional drift detection and online learning paradigms, our approach requires no prior assumptions about drift types and avoids frequent model updates. Extensive experiments across seven classification benchmarks demonstrate that, compared to state-of-the-art baselines, our method significantly improves the accuracy–cost trade-off: it reduces spurious retraining events by 42% while maintaining robust performance under continuous distribution shift, sparse monitoring signals, and stringent cost constraints—validating its effectiveness and practicality in dynamic, resource-constrained environments.

0 citationsRead paper

Understanding the Design Principles of Link Prediction in Directed Settings

Feb 20, 2025

This study addresses directed link prediction, tackling the limitation of existing graph representation learning methods—which predominantly assume undirected graphs and thus fail to capture directional interactions. We propose the first heuristic paradigm explicitly designed for directed link prediction. By reformulating classical heuristics (e.g., common neighbors, Adamic-Adar, and Katz) with direction-aware neighborhood aggregation and edge-level feature encoding, we construct a lightweight framework that requires neither message passing nor end-to-end training. Evaluated on multiple real-world directed graph benchmarks, our method consistently outperforms conventional heuristics and state-of-the-art GNNs originally designed for undirected graphs. These results empirically validate the critical importance of explicit directional modeling and, for the first time, demonstrate systematic superiority of heuristic approaches over mainstream GNNs in directed link prediction.

0 citationsRead paper

Recent publications

Latest Papers

Improving Function Space Flow Matching with Kernel Optimal Transport

Sep 29, 2026

This study addresses the inefficient transport paths and lack of geometric structure caused by independent endpoint pairing in generative models over function spaces. To this end, we propose Kernel Flow Matching, which replaces random pairing with entropic optimal transport under the Hilbert-Sinkhorn divergence. By introducing a kernel-induced cost, the method enables infinite-dimensional optimal transport to improve function distribution learning. Theoretically, we establish target boundedness and discretization invariance while isolating irreducible error terms. Empirically, our approach significantly outperforms baselines such as FFM on time series forecasting and PDE benchmarks, and its effectiveness is further validated in modeling turbulent Navier-Stokes equations.

0 citationsRead paper

A Unified Uncertainty Representation for Graph Neural Networks via Doubly-Spectral Stochastic Expansion

Sep 28, 2026

This study addresses the limitation of existing graph neural networks (GNNs) that require separate models for calibration, out-of-distribution (OOD) detection, and robustness tasks. To this end, we propose DSS-GNN, a unified framework that leverages dual spectral stochastic expansion—integrating graph Fourier filtering with orthogonal polynomial chaos expansion—to characterize uncertainty comprehensively. Coupled with energy-based scoring, this approach enables a single model to jointly perform prediction, calibration, and OOD detection within a hybrid deployment setting. Extensive experiments demonstrate that DSS-GNN achieves the lowest Brier scores across 14 benchmarks and attains state-of-the-art shifted accuracy on 7 GOOD benchmarks. These results confirm that the proposed framework effectively resolves the multi-model fragmentation problem in GNN uncertainty quantification, offering a cohesive and highly performant solution for reliable graph representation learning.

0 citationsRead paper

Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations

Jun 07, 2025

Graph Neural Networks (GNNs) struggle to reliably quantify predictive uncertainty under distributional shift, primarily because conventional approaches fail to jointly model the dual stochasticity inherent in graph structure and label distribution. Method: We establish, for the first time, a theoretical analogy between stochastic partial differential equation (SPDE)-driven Matérn Gaussian processes and GNN message passing. Based on this, we propose SPDE-GNN: a framework that employs SPDEs as the kernel for structural-aware stochastic message passing; incorporates Matérn priors for joint spatiotemporal uncertainty modeling; and enables tunable smoothness of the covariance kernel. Contribution/Results: Coupled with structural-aware noise injection and an out-of-distribution (OOD) evaluation framework, SPDE-GNN achieves significant improvements over state-of-the-art methods across diverse graph OOD detection tasks—particularly maintaining high robustness and calibration accuracy even when label informativeness varies substantially.

0 citationsRead paper

When to retrain a machine learning model

May 20, 2025

In real-world deployment, deciding when to retrain machine learning models faces three key challenges: sparse observational samples, unknown characteristics of data distribution shifts, and the difficulty of balancing retraining cost against performance degradation. This paper proposes the first retraining decision framework grounded in performance evolution prediction and uncertainty modeling. It explicitly jointly models performance decay trends, predictive uncertainty bounds, and temporal performance dynamics, and incorporates a cost-aware decision mechanism. Departing from conventional drift detection and online learning paradigms, our approach requires no prior assumptions about drift types and avoids frequent model updates. Extensive experiments across seven classification benchmarks demonstrate that, compared to state-of-the-art baselines, our method significantly improves the accuracy–cost trade-off: it reduces spurious retraining events by 42% while maintaining robust performance under continuous distribution shift, sparse monitoring signals, and stringent cost constraints—validating its effectiveness and practicality in dynamic, resource-constrained environments.

0 citationsRead paper

Understanding the Design Principles of Link Prediction in Directed Settings

Feb 20, 2025

This study addresses directed link prediction, tackling the limitation of existing graph representation learning methods—which predominantly assume undirected graphs and thus fail to capture directional interactions. We propose the first heuristic paradigm explicitly designed for directed link prediction. By reformulating classical heuristics (e.g., common neighbors, Adamic-Adar, and Katz) with direction-aware neighborhood aggregation and edge-level feature encoding, we construct a lightweight framework that requires neither message passing nor end-to-end training. Evaluated on multiple real-world directed graph benchmarks, our method consistently outperforms conventional heuristics and state-of-the-art GNNs originally designed for undirected graphs. These results empirically validate the critical importance of explicit directional modeling and, for the first time, demonstrate systematic superiority of heuristic approaches over mainstream GNNs in directed link prediction.

0 citationsRead paper