Provably Extending PageRank-based Local Clustering Algorithm to Weighted Directed Graphs with Self-Loops and to Hypergraphs

Local clustering aims to find a compact cluster near the given starting instances. This work focuses on graph local clustering, which has broad applications beyond graphs because of the internal connectivities within various modalities. While most existing studies on local graph clustering adopt the discrete graph setting (i.e., unweighted graphs without self-loops), real-world graphs can be more complex. In this paper, we extend the non-approximating Andersen-Chung-Lang ("ACL") algorithm beyond discrete graphs and generalize its quadratic optimality to a wider range of graphs, including weighted, directed, and self-looped graphs and hypergraphs. Specifically, leveraging PageRank, we propose two algorithms: GeneralACL for graphs and HyperACL for hypergraphs. We theoretically prove that, under two mild conditions, both algorithms can identify a quadratically optimal local cluster in terms of conductance with at least 1/2 probability. On the property of hypergraphs, we address a fundamental gap in the literature by defining conductance for hypergraphs from the perspective of hypergraph random walks. Additionally, we provide experiments to validate our theoretical findings.

Marked Temporal Bayesian Flow Point Processes

Marked event data captures events by recording their continuous-valued occurrence timestamps along with their corresponding discrete-valued types. They have appeared in various real-world scenarios such as social media, financial transactions, and healthcare records, and have been effectively modeled through Marked Temporal Point Process (MTPP) models. Recently, developing generative models for these MTPP models have seen rapid development due to their powerful generative capability and less restrictive functional forms. However, existing generative MTPP models are usually challenged in jointly modeling events' timestamps and types since: (1) mainstream methods design the generative mechanisms for timestamps only and do not include event types; (2) the complex interdependence between the timestamps and event types are overlooked. In this paper, we propose a novel generative MTPP model called BMTPP. Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach. Additionally, by adding joint noise to the marked temporal data space, BMTPP effectively captures and explicitly reveals the interdependence between timestamps and event types. Extensive experiments validate the superiority of our approach over other state-of-the-art models and its ability to effectively capture marked-temporal interdependence.

Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequality

Hypergraphs naturally arise when studying group relations and have been widely used in the field of machine learning. There has not been a unified formulation of hypergraphs, yet the recently proposed edge-dependent vertex weights (EDVW) modeling is one of the most generalized modeling methods of hypergraphs, i.e., most existing hypergraphs can be formulated as EDVW hypergraphs without any information loss to the best of our knowledge. However, the relevant algorithmic developments on EDVW hypergraphs remain nascent: compared to spectral graph theories, the formulations are incomplete, the spectral clustering algorithms are not well-developed, and one result regarding hypergraph Cheeger Inequality is even incorrect. To this end, deriving a unified random walk-based formulation, we propose our definitions of hypergraph Rayleigh Quotient, NCut, boundary/cut, volume, and conductance, which are consistent with the corresponding definitions on graphs. Then, we prove that the normalized hypergraph Laplacian is associated with the NCut value, which inspires our HyperClus-G algorithm for spectral clustering on EDVW hypergraphs. Finally, we prove that HyperClus-G can always find an approximately linearly optimal partitioning in terms of Both NCut and conductance. Additionally, we provide extensive experiments to validate our theoretical findings from an empirical perspective.

Federated Neural Nonparametric Point Processes

Temporal point processes (TPPs) are effective for modeling event occurrences over time, but they struggle with sparse and uncertain events in federated systems, where privacy is a major concern. To address this, we propose \textit{FedPP}, a Federated neural nonparametric Point Process model. FedPP integrates neural embeddings into Sigmoidal Gaussian Cox Processes (SGCPs) on the client side, which is a flexible and expressive class of TPPs, allowing it to generate highly flexible intensity functions that capture client-specific event dynamics and uncertainties while efficiently summarizing historical records. For global aggregation, FedPP introduces a divergence-based mechanism that communicates the distributions of SGCPs' kernel hyperparameters between the server and clients, while keeping client-specific parameters local to ensure privacy and personalization. FedPP effectively captures event uncertainty and sparsity, and extensive experiments demonstrate its superior performance in federated settings, particularly with KL divergence and Wasserstein distance-based global aggregation.

GaussianStego: A Generalizable Stenography Pipeline for Generative 3D Gaussians Splatting

Recent advancements in large generative models and real-time neural rendering using point-based techniques pave the way for a future of widespread visual data distribution through sharing synthesized 3D assets. However, while standardized methods for embedding proprietary or copyright information, either overtly or subtly, exist for conventional visual content such as images and videos, this issue remains unexplored for emerging generative 3D formats like Gaussian Splatting. We present GaussianStego, a method for embedding steganographic information in the rendering of generated 3D assets. Our approach employs an optimization framework that enables the accurate extraction of hidden information from images rendered using Gaussian assets derived from large models, while maintaining their original visual quality. We conduct preliminary evaluations of our method across several potential deployment scenarios and discuss issues identified through analysis. GaussianStego represents an initial exploration into the novel challenge of embedding customizable, imperceptible, and recoverable information within the renders produced by current 3D generative models, while ensuring minimal impact on the rendered content's quality.

EndoSparse: Real-Time Sparse View Synthesis of Endoscopic Scenes using Gaussian Splatting

3D reconstruction of biological tissues from a collection of endoscopic images is a key to unlock various important downstream surgical applications with 3D capabilities. Existing methods employ various advanced neural rendering techniques for photorealistic view synthesis, but they often struggle to recover accurate 3D representations when only sparse observations are available, which is usually the case in real-world clinical scenarios. To tackle this {sparsity} challenge, we propose a framework leveraging the prior knowledge from multiple foundation models during the reconstruction process, dubbed as \textit{EndoSparse}. Experimental results indicate that our proposed strategy significantly improves the geometric and appearance quality under challenging sparse-view conditions, including using only three views. In rigorous benchmarking experiments against state-of-the-art methods, \textit{EndoSparse} achieves superior results in terms of accurate geometry, realistic appearance, and rendering efficiency, confirming the robustness to sparse-view limitations in endoscopic reconstruction. \textit{EndoSparse} signifies a steady step towards the practical deployment of neural 3D reconstruction in real-world clinical scenarios. Project page: https://endo-sparse.github.io/.

LGS: A Light-weight 4D Gaussian Splatting for Efficient Surgical Scene Reconstruction

The advent of 3D Gaussian Splatting (3D-GS) techniques and their dynamic scene modeling variants, 4D-GS, offers promising prospects for real-time rendering of dynamic surgical scenarios. However, the prerequisite for modeling dynamic scenes by a large number of Gaussian units, the high-dimensional Gaussian attributes and the high-resolution deformation fields, all lead to serve storage issues that hinder real-time rendering in resource-limited surgical equipment. To surmount these limitations, we introduce a Lightweight 4D Gaussian Splatting framework (LGS) that can liberate the efficiency bottlenecks of both rendering and storage for dynamic endoscopic reconstruction. Specifically, to minimize the redundancy of Gaussian quantities, we propose Deformation-Aware Pruning by gauging the impact of each Gaussian on deformation. Concurrently, to reduce the redundancy of Gaussian attributes, we simplify the representation of textures and lighting in non-crucial areas by pruning the dimensions of Gaussian attributes. We further resolve the feature field redundancy caused by the high resolution of 4D neural spatiotemporal encoder for modeling dynamic scenes via a 4D feature field condensation. Experiments on public benchmarks demonstrate efficacy of LGS in terms of a compression rate exceeding 9 times while maintaining the pleasing visual quality and real-time rendering efficiency. LGS confirms a substantial step towards its application in robotic surgical services.

U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation

U-Net has become a cornerstone in various visual applications such as image segmentation and diffusion probability models. While numerous innovative designs and improvements have been introduced by incorporating transformers or MLPs, the networks are still limited to linearly modeling patterns as well as the deficient interpretability. To address these challenges, our intuition is inspired by the impressive results of the Kolmogorov-Arnold Networks (KANs) in terms of accuracy and interpretability, which reshape the neural network learning via the stack of non-linear learnable activation functions derived from the Kolmogorov-Anold representation theorem. Specifically, in this paper, we explore the untapped potential of KANs in improving backbones for vision tasks. We investigate, modify and re-design the established U-Net pipeline by integrating the dedicated KAN layers on the tokenized intermediate representation, termed U-KAN. Rigorous medical image segmentation benchmarks verify the superiority of U-KAN by higher accuracy even with less computation cost. We further delved into the potential of U-KAN as an alternative U-Net noise predictor in diffusion models, demonstrating its applicability in generating task-oriented model architectures. These endeavours unveil valuable insights and sheds light on the prospect that with U-KAN, you can make strong backbone for medical image segmentation and generation. Project page: https://yes-ukan.github.io/

FedSI: Federated Subnetwork Inference for Efficient Uncertainty Quantification

While deep neural networks (DNNs) based personalized federated learning (PFL) is demanding for addressing data heterogeneity and shows promising performance, existing methods for federated learning (FL) suffer from efficient systematic uncertainty quantification. The Bayesian DNNs-based PFL is usually questioned of either over-simplified model structures or high computational and memory costs. In this paper, we introduce FedSI, a novel Bayesian DNNs-based subnetwork inference PFL framework. FedSI is simple and scalable by leveraging Bayesian methods to incorporate systematic uncertainties effectively. It implements a client-specific subnetwork inference mechanism, selects network parameters with large variance to be inferred through posterior distributions, and fixes the rest as deterministic ones. FedSI achieves fast and scalable inference while preserving the systematic uncertainties to the fullest extent. Extensive experiments on three different benchmark datasets demonstrate that FedSI outperforms existing Bayesian and non-Bayesian FL baselines in heterogeneous FL scenarios.

Endora: Video Generation Models as Endoscopy Simulators

Generative models hold promise for revolutionizing medical education, robot-assisted surgery, and data augmentation for machine learning. Despite progress in generating 2D medical images, the complex domain of clinical video generation has largely remained untapped.This paper introduces \model, an innovative approach to generate medical videos that simulate clinical endoscopy scenes. We present a novel generative model design that integrates a meticulously crafted spatial-temporal video transformer with advanced 2D vision foundation model priors, explicitly modeling spatial-temporal dynamics during video generation. We also pioneer the first public benchmark for endoscopy simulation with video generation models, adapting existing state-of-the-art methods for this endeavor.Endora demonstrates exceptional visual quality in generating endoscopy videos, surpassing state-of-the-art methods in extensive testing. Moreover, we explore how this endoscopy simulator can empower downstream video analysis tasks and even generate 3D medical scenes with multi-view consistency. In a nutshell, Endora marks a notable breakthrough in the deployment of generative AI for clinical endoscopy research, setting a substantial stage for further advances in medical content generation. For more details, please visit our project page: https://endora-medvidgen.github.io/.