arXiv subjects

Xingqin Qi

Publications and source records attributed to Xingqin Qi.

11 recordsLinked to original sources

arXiv2026

Proper conflict-free choosability of sparse graphs with girth at least seven

A proper conflict-free coloring is a proper vertex coloring in which every non-isolated vertex has a color appearing exactly once in its open neighborhood. We prove that every finite simple graph with girth at least 7 and maximum average degree less than 8/3 admits a proper conflict-free coloring from arbitrary vertex lists of size at least the vertex degree plus 2. Consequently, every planar graph of girth at least 8 is proper conflict-free (degree+2)-choosable, improving the sufficient girth bound of 9 obtained from the earlier 18/7 maximum-average-degree theorem. The proof uses local extension lemmas for short threads, including threads with a common boundary endpoint. Two-element control sets and an incidence count yield a weighted thread inequality, which supplies the required bound on the charge sent by each vertex in a discharging argument.

math.CO↗

arXiv2026

From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.

cs.LG↗

arXiv2026

Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation

Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored. Unlike pairwise graphs, uncertainty in hypergraphs arises not only from noisy attributes and ambiguous labels, but also from variations in node-hyperedge incidence structures and complex higher-order dependencies. Existing approaches mainly estimate uncertainty from final predictions or rely on computationally expensive ensembles and Bayesian inference, limiting their ability to capture uncertainty evolution during representation learning. In this paper, we propose Hypergraph Neural Stochastic Diffusion(HyperNSD), a stochastic differential equation framework for uncertainty estimation on hypergraphs. HyperNSD models hypergraph representations as stochastic processes evolving over node-hyperedge incidence structures. A learnable drift function captures deterministic higher-order diffusion dynamics, while a learnable stochastic forcing function characterizes structural ambiguity and representation noise. Predictive uncertainty is directly quantified through the variability of stochastic representation trajectories, providing an intrinsic uncertainty measure beyond post-hoc confidence scores. We formulate HyperNSD with neural drift and diffusion networks, enabling joint learning of prediction and uncertainty propagation. Theoretical analyses establish well posedness, perturbation stability,permutation equivariance, and numerical convergence of the proposed stochastic dynamics. Experiments on multiple hypergraph benchmarks demonstrate that HyperNSD achieves reliable uncertainty estimation for out-of-distribution and misclassification detection while preserving competitive prediction accuracy. These results provide a principled stochastic-dynamical framework for trustworthy higher-order representation learning.

cs.LG↗

arXiv2026

Interpretable Information-Decomposed Brain Graph Learning for fMRI-based Disease Diagnosis

Resting-state functional magnetic resonance imaging (rs-fMRI) has enabled non-invasive mapping of functional brain interactions for computer-aided diagnosis, yet most existing approaches reduce inter-regional relationships to correlation-based edge weights. Such representations capture co-fluctuation strength but obscure how information is shared across brain regions. Because brain disorders may disrupt not only connectivity strength but also the organization of redundancy, uniqueness and synergy, traditional functional connectivity may miss disease-relevant information structures. Here we introduce IID-GCN, an interpretable graph learning framework that decomposes rs-fMRI interactions into redundancy, uniqueness and synergy graphs using partial entropy decomposition. These information-specific graphs separately characterize shared, region-specific and jointly emergent components of brain activity. A multi-channel graph convolutional network then integrates the decomposed graphs through edge recalibration, cross-information interaction, ROI-attention readout and channel-attentive fusion. Across three datasets, IID-GCN consistently captures complementary diagnostic information beyond traditional functional connectivity. The learned information profiles reveal disorder-specific patterns of altered redundancy, uniqueness and synergy, suggesting that brain diseases reshape functional information organization rather than merely changing connection strength. These results establish information-decomposed brain graphs as an interpretable representation for rs-fMRI-based diagnosis. Our code is available at https://github.com/Zdy12/IID-GCN.

q-bio.NC↗

arXiv2026

Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing

Hypergraph neural networks (HGNNs) have shown remarkable potential in modeling high-order relationships that naturally arise in many real-world data domains. However, existing HGNNs often suffer from shallow propagation, oversmoothing, and limited adaptability to complex hypergraph structures. In this paper, we propose Hypergraph Neural Diffusion (HND), a novel framework that unifies nonlinear diffusion equations with neural message passing on hypergraphs. HND is grounded in a continuous-time hypergraph diffusion equation, formulated via hypergraph gradient and divergence operators, and modulated by a learnable, structure-aware coefficient matrix over hyperedge-node pairs. This partial differential equation (PDE) based formulation provides a physically interpretable view of hypergraph learning, where feature propagation is understood as an anisotropic diffusion process governed by local inconsistency and adaptive diffusion coefficient. From this perspective, neural message passing becomes a discretized gradient flow that progressively minimizes a diffusion energy functional. We derive rigorous theoretical guarantees, including energy dissipation, solution boundedness via a discrete maximum principle, and stability under explicit and implicit numerical schemes. The HND framework supports a variety of integration strategies such as non-adaptive-step (like Runge-Kutta) and adaptive-step solvers, enabling the construction of deep, stable, and interpretable architectures. Extensive experiments on benchmark datasets demonstrate that HND achieves competitive performance. Our results highlight the power of PDE-inspired design in enhancing the stability, expressivity, and interpretability of hypergraph learning.

cs.LG↗

arXiv2026

Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach

Hypergraph neural networks (HGNNs) have demonstrated strong capabilities in modeling complex higher-order relationships. However, existing HGNNs often suffer from over-smoothing as the number of layers increases and lack effective control over message passing among nodes. Inspired by the theory of Ricci flow in differential geometry, we theoretically establish that introducing discrete Ricci flow into hypergraph structures can effectively regulate node feature evolution and thereby alleviate over-smoothing. Building on this insight, we propose Ricci Flow-guided Hypergraph Neural Diffusion(RFHND), a novel message passing paradigm for hypergraphs guided by discrete Ricci flow. Specifically, RFHND is based on a PDE system that describes the continuous evolution of node features on hypergraphs and adaptively regulates the rate of information diffusion at the geometric level, preventing feature homogenization and producing high-quality node representations. Experimental results show that RFHND significantly outperforms existing methods across multiple benchmark datasets and demonstrates strong robustness, while also effectively mitigating over-smoothing.

cs.LG↗

arXiv2026

HOI-Brain: a novel multi-channel transformers framework for brain disorder diagnosis by accurately extracting signed higher-order interactions from fMRI

Accurately characterizing higher-order interactions of brain regions and extracting interpretable organizational patterns from Functional Magnetic Resonance Imaging data is crucial for brain disease diagnosis. Current graph-based deep learning models primarily focus on pairwise or triadic patterns while neglecting signed higher-order interactions, limiting comprehensive understanding of brain-wide communication. We propose HOI-Brain, a novel computational framework leveraging signed higher-order interactions and organizational patterns in fMRI data for brain disease diagnosis. First, we introduce a co-fluctuation measure based on Multiplication of Temporal Derivatives to detect higher-order interactions with temporal resolution. We then distinguish positive and negative synergistic interactions, encoding them in signed weighted simplicial complexes to reveal brain communication insights. Using Persistent Homology theory, we apply two filtration processes to these complexes to extract signed higher-dimensional neural organizations spatiotemporally. Finally, we propose a multi-channel brain Transformer to integrate heterogeneous topological features. Experiments on Alzheimer' s disease, Parkinson' s syndrome, and autism spectrum disorder datasets demonstrate our framework' s superiority, effectiveness, and interpretability. The identified key brain regions and higher-order patterns align with neuroscience literature, providing meaningful biological insights.

q-bio.NC↗

arXiv2025

Modeling Hypergraph Using Large Language Models

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to high-quality, large-scale real-world hypergraph data. Yet, compared to traditional pairwise graphs, real hypergraph datasets remain scarce in both scale and diversity. This shortage significantly limits the development and evaluation of advanced hypergraph learning algorithms. Therefore, how to quickly generate large-scale hypergraphs that conform to the characteristics of real networks is a crucial task that has not received sufficient attention. Motivated by recent advances in large language models (LLMs), particularly their capabilities in semantic reasoning, structured generation, and simulating human behavior, we investigate whether LLMs can facilitate hypergraph generation from a fundamentally new perspective. We introduce HyperLLM, a novel LLM-driven hypergraph generator that simulates the formation and evolution of hypergraphs through a multi-agent collaboration. The framework integrates prompts and structural feedback mechanisms to ensure that the generated hypergraphs reflect key real-world patterns. Extensive experiments across diverse datasets demonstrate that HyperLLM achieves superior fidelity to structural and temporal hypergraph patterns, while requiring minimal statistical priors. Our findings suggest that LLM-based frameworks offer a promising new direction for hypergraph modeling.

cs.SI↗

arXiv2025

Extracting Interpretable Higher-Order Topological Features across Multiple Scales for Alzheimer's Disease Classification

Brain network topology, derived from functional magnetic resonance imaging (fMRI), holds promise for improving Alzheimer's disease (AD) diagnosis. Current methods primarily focus on lower-order topological features, often overlooking the significance of higher-order features such as connected components, cycles, and cavities. These higher-order features are critical for understanding normal brain function and have been increasingly linked to the pathological mechanisms of AD. However, their quantification for diagnosing AD is hindered by their inherent nonlinearity and stochasticity in the brain. This paper introduces a novel framework for diagnosing Alzheimer's disease that uses persistent homology to extract higher-order topological features from fMRI data. It also introduces four quantitative methods that capture subtle, multiscale geometric variations in functional brain networks associated with AD. Our experimental results demonstrate that this framework significantly outperforms existing methods in AD classification. Extensive ablation studies and interpretability analysis confirm the effectiveness of our framework. Our study also reveals that the number of cycles or cavities significantly decrease in AD patients. The extracted key brain regions derived from cycles and cavities align with domain knowledge in neuroscience literature and provide direct and insightful findings. This study highlights the potential of higher-order topological features for early AD detection and significantly advances the field of brain topology analysis in neurodegenerative disease research.

math.GT↗

arXiv2024

Defensive Alliances in Signed Networks

The analysis of (social) networks and multi-agent systems is a central theme in Artificial Intelligence. Some line of research deals with finding groups of agents that could work together to achieve a certain goal. To this end, different notions of so-called clusters or communities have been introduced in the literature of graphs and networks. Among these, defensive alliance is a kind of quantitative group structure. However, all studies on the alliance so for have ignored one aspect that is central to the formation of alliances on a very intuitive level, assuming that the agents are preconditioned concerning their attitude towards other agents: they prefer to be in some group (alliance) together with the agents they like, so that they are happy to help each other towards their common aim, possibly then working against the agents outside of their group that they dislike. Signed networks were introduced in the psychology literature to model liking and disliking between agents, generalizing graphs in a natural way. Hence, we propose the novel notion of a defensive alliance in the context of signed networks. We then investigate several natural algorithmic questions related to this notion. These, and also combinatorial findings, connect our notion to that of correlation clustering, which is a well-established idea of finding groups of agents within a signed network. Also, we introduce a new structural parameter for signed graphs, signed neighborhood diversity snd, and exhibit a parameterized algorithm that finds a smallest defensive alliance in a signed graph.

cs.CC↗

arXiv2023

Offensive Alliances in Signed Graphs

Signed graphs have been introduced to enrich graph structures expressing relationships between persons or general social entities, introducing edge signs to reflect the nature of the relationship, e.g., friendship or enmity. Independently, offensive alliances have been defined and studied for undirected, unsigned graphs. We join both lines of research and define offensive alliances in signed graphs, hence considering the nature of relationships. Apart from some combinatorial results, mainly on k-balanced and k-anti-balanced signed graphs (where the latter is a newly introduced family of signed graphs), we focus on the algorithmic complexity of finding smallest offensive alliances, looking at a number of parameterizations. While the parameter solution size leads to an FPT result for unsigned graphs, we obtain W[2]-completeness for the signed setting. We introduce new parameters for signed graphs, e.g., distance to weakly balanced signed graphs, that could be of independent interest. We show that these parameters yield FPT results. Here, we make use of the recently introduced parameter neighborhood diversity for signed graphs.

cs.CC↗