arXiv subjects

Haifang Cao

Publications and source records attributed to Haifang Cao.

4 recordsLinked to original sources

arXiv2026

Topology-Adaptive Hyperbolic Graph Attention Networks Guided by the Hyperbolic Sombor Index

Hyperbolic geometry has emerged as a principled space for representing hierarchical graphs. However, existing hyperbolic graph neural networks typically rely on shared curvature configurations and feature-driven attention, failing to explicitly exploit local hierarchical topological patterns. To bridge this gap, we introduce the Hyperbolic Sombor Index (HSO) as a lightweight structural prior for capturing hierarchy-indicative degree stratification. Building on this, we propose \textbf{HSO-GAT}, a topology-adaptive hyperbolic graph attention network that unifies geometric adaptation and message propagation. Specifically, it comprises two complementary modules: HSO-Guided Local Curvature Adaptation, which performs adaptive node-wise geometric scaling from aggregated node-level HSO signals, and HSO-Gated Hyperbolic Graph Attention, which enables structure-aware message passing through feature-conditioned gating. Theoretically, we establish the monotonic sensitivity of edge-level HSO to degree imbalance and analyze the validity and radial scaling properties of node-adaptive hyperbolic mappings. Extensive experiments on eight benchmark datasets demonstrate that HSO-GAT consistently achieves state-of-the-art performance in both node classification and link prediction tasks.

cs.LG↗

arXiv2026

SAGE: Source-Anchored Guidance via Frequency Equalization for Hierarchical RGB-T Alignment and Fusion

Spatial misregistration and cross-modal discrepancies often cause ghosting, structural blurring, and content imbalance in RGB-T fusion. Existing methods typically decouple appearance adaptation, geometric alignment, and information fusion, limiting dependency propagation across stages. We propose Source-Anchored Guidance via Frequency Equalization for Hierarchical RGB-T Alignment and Fusion (SAGE), a unified framework integrating frequency equalization, hierarchical alignment, and subband fusion. SAGE employs invertible joint encoding and source-specific low-frequency modulation to derive structural and gain guidance while preserving source information. Hierarchical frequency collaborative alignment estimates global affine geometry from low-frequency approximations and transfers geometric and contextual cues to high-frequency correlation reasoning for reliability-aware residual refinement. Guided subband fusion jointly aggregates the aligned frequency coefficients under propagated source and alignment guidance, coordinates complementary low- and high-frequency information, and reconstructs the fused image through the inverse wavelet transform. Extensive experiments on RGB-T datasets with real-world and synthetic misalignments demonstrate consistently competitive performance in alignment and fusion, validating the effectiveness of source-anchored guidance for weakly registered RGB-T images.

cs.CV↗

arXiv2026

Hyperbolic Cycle Alignment for Infrared-Visible Image Fusion

Image fusion synthesizes complementary information from multiple sources, mitigating the inherent limitations of unimodal imaging systems. Accurate image registration is essential for effective multi-source data fusion. However, existing registration methods, often based on image translation in Euclidean space, fail to handle cross-modal misalignment effectively, resulting in suboptimal alignment and fusion quality. To overcome this limitation, we explore image alignment in non-Euclidean space and propose a Hyperbolic Cycle Alignment Network (Hy-CycleAlign). To the best of our knowledge, Hy-CycleAlign is the first image registration method based on hyperbolic space. It introduces a dual-path cross-modal cyclic registration framework, in which a forward registration network aligns cross-modal inputs, while a backward registration network reconstructs the original image, forming a closed-loop registration structure with geometric consistency. Additionally, we design a Hyperbolic Hierarchy Contrastive Alignment (H$^{2}$CA) module, which maps images into hyperbolic space and imposes registration constraints, effectively reducing interference caused by modality discrepancies. We further analyze image registration in both Euclidean and hyperbolic spaces, demonstrating that hyperbolic space enables more sensitive and effective multi-modal image registration. Extensive experiments on misaligned multi-modal images demonstrate that our method significantly outperforms existing approaches in both image alignment and fusion. Our code will be publicly available.

cs.CV↗

arXiv2026

Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning

Graph-structured data typically exhibits complex topological heterogeneity, making it difficult to model accurately within a single Riemannian manifold. While emerging mixed-curvature methods attempt to capture such diversity, they often rely on implicit, task-driven routing that lacks fundamental geometric grounding. To address this challenge, we propose a Geometric Mixture-of-Experts framework (GeoMoE) that adaptively fuses node representations across diverse Riemannian spaces to better accommodate multi-scale topological structures. At its core, GeoMoE leverages Ollivier-Ricci Curvature (ORC) as an intrinsic geometric prior to orchestrate the collaboration of specialized experts. Specifically, we design a graph-aware gating network that assigns node-specific fusion weights, regularized by a curvature-guided alignment loss to ensure interpretable and geometry-consistent routing. Additionally, we introduce a curvature-aware contrastive objective that promotes geometric discriminability by constructing positive and negative pairs according to curvature consistency. Extensive experiments on six benchmark datasets demonstrate that GeoMoE outperforms state-of-the-art baselines across diverse graph types.

cs.LG↗