Jiaze Li

Jiaze Li, Michael T. Schaub, Leto Peel

Extending community detection from pairwise networks to hypergraphs introduces fundamental theoretical challenges. Hypergraphs exhibit structural heterogeneity with no direct graph analogue: hyperedges of varying orders can connect nodes across communities in diverse configurations, introducing new trade-offs in defining and detecting community structure. We address these challenges by developing a unified framework for community detection in non-uniform hypergraphs under the Hypergraph Stochastic Block Model. We introduce a general signal-to-noise ratio that enables a quantitative analysis of trade-offs unique to higher-order networks, such as which hypergedges we choose to split across communities and how we choose to split them. Building on this framework, we derive a Bethe Hessian operator for non-uniform hypergraphs that provides efficient spectral clustering with principled model selection. We characterize the resulting spectral detectability threshold and compare it to belief propagation limits, showing the methods coincide for uniform hypergraphs but diverge in non-uniform settings. Synthetic experiments confirm our analytical predictions and reveal systematic biases toward preserving higher-order and balanced-shape hyperedges. Application to empirical data demonstrates the practical relevance of these higher-order detectability trade-offs in real-world systems.

Yuji Wang, Haoran Xu, Yong Liu et al.

Reference Audio-Visual Segmentation (Ref-AVS) aims to provide a pixel-wise scene understanding in Language-aided Audio-Visual Scenes (LAVS). This task requires the model to continuously segment objects referred to by text and audio from a video. Previous dual-modality methods always fail due to the lack of a third modality and the existing triple-modality method struggles with spatio-temporal consistency, leading to the target shift of different frames. In this work, we introduce a novel framework, termed SAM2-LOVE, which integrates textual, audio, and visual representations into a learnable token to prompt and align SAM2 for achieving Ref-AVS in the LAVS. Technically, our approach includes a multimodal fusion module aimed at improving multimodal understanding of SAM2, as well as token propagation and accumulation strategies designed to enhance spatio-temporal consistency without forgetting historical information. We conducted extensive experiments to demonstrate that SAM2-LOVE outperforms the SOTA by 8.5\% in $\mathcal{J\&F}$ on the Ref-AVS benchmark and showcase the simplicity and effectiveness of the components. Our code will be available here.

Jiaze Li, Zhengyu Wen, Luo Zhang et al.

The 3D Gaussian Splatting technique has significantly advanced the construction of radiance fields from multi-view images, enabling real-time rendering. While point-based rasterization effectively reduces computational demands for rendering, it often struggles to accurately reconstruct the geometry of the target object, especially under strong lighting. To address this challenge, we introduce a novel approach that combines octree-based implicit surface representations with Gaussian splatting. Our method consists of four stages. Initially, it reconstructs a signed distance field (SDF) and a radiance field through volume rendering, encoding them in a low-resolution octree. The initial SDF represents the coarse geometry of the target object. Subsequently, it introduces 3D Gaussians as additional degrees of freedom, which are guided by the SDF. In the third stage, the optimized Gaussians further improve the accuracy of the SDF, allowing it to recover finer geometric details compared to the initial SDF obtained in the first stage. Finally, it adopts the refined SDF to further optimize the 3D Gaussians via splatting, eliminating those that contribute little to visual appearance. Experimental results show that our method, which leverages the distribution of 3D Gaussians with SDFs, reconstructs more accurate geometry, particularly in images with specular highlights caused by strong lighting.

Michael T. Schaub, Jiaze Li, Leto Peel

Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have included identifying fundamental limits of detectability by formally defining community structure using probabilistic generative models. Detecting hierarchical community structure introduces additional challenges alongside those inherited from community detection. Here we present a theoretical study on hierarchical community structure in networks, which has thus far not received the same rigorous attention. We address the following questions: 1) How should we define a hierarchy of communities? 2) How do we determine if there is sufficient evidence of a hierarchical structure in a network? and 3) How can we detect hierarchical structure efficiently? We approach these questions by introducing a definition of hierarchy based on the concept of stochastic externally equitable partitions and their relation to probabilistic models, such as the popular stochastic block model. We enumerate the challenges involved in detecting hierarchies and, by studying the spectral properties of hierarchical structure, present an efficient and principled method for detecting them.