Quan Zhao

Yuntao Wang, Yanghe Pan, Zhou Su et al.

With the rapid advancement of large models (LMs), the development of general-purpose intelligent agents powered by LMs has become a reality. It is foreseeable that in the near future, LM-driven general AI agents will serve as essential tools in production tasks, capable of autonomous communication and collaboration without human intervention. This paper investigates scenarios involving the autonomous collaboration of future LM agents. We review the current state of LM agents, the key technologies enabling LM agent collaboration, and the security and privacy challenges they face during cooperative operations. To this end, we first explore the foundational principles of LM agents, including their general architecture, key components, enabling technologies, and modern applications. We then discuss practical collaboration paradigms from data, computation, and knowledge perspectives to achieve connected intelligence among LM agents. After that, we analyze the security vulnerabilities and privacy risks associated with LM agents, particularly in multi-agent settings, examining underlying mechanisms and reviewing current and potential countermeasures. Lastly, we propose future research directions for building robust and secure LM agent ecosystems.

Harald Garcke, Robert Nürnberg, Quan Zhao

We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with boundary. The presented scheme is based on a new geometric partial differential equation (PDE) that combines an evolution equation for the mean curvature with a separate equation that prescribes the tangential velocity. The mean curvature is used to determine the normal velocity within the gradient flow structure, thus guaranteeing an unconditional energy stability for the discrete solution upon suitable discretization. We introduce a novel weak formulation for this geometric PDE, in which different types of boundary conditions can be naturally enforced. We further discretize the weak formulation to obtain a fully discrete parametric finite element method, for which well-posedness can be rigorously shown. Moreover, the constructed scheme admits an unconditional stability estimate in terms of the discrete energy. Extensive numerical experiments are reported to showcase the accuracy and robustness of the proposed method for computing Willmore flow of both curves in $\mathbb{R}^2$ and surfaces in $\mathbb{R}^3$.

Harald Garcke, Robert Nürnberg, Quan Zhao

We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous curvature effects. The axisymmetric setting allows us to formulate our schemes in terms of the generating curve of the considered surface. We propose a novel weak formulation, that combines an evolution equation for the surface's mean curvature and the curvature identity of the generating curve. The mean curvature is used to describe the gradient flow structure, which enables an unconditional stability result for the discrete solutions. The generating curve's curvature, on the other hand, describes the surface's in-plane principal curvature and plays the role of a Lagrange multiplier for an equidistribution property on the discrete level. We introduce two fully discrete schemes and prove their unconditional stability. Numerical results are provided to confirm the convergence, stability and equidistribution properties of the introduced schemes.

Desheng Cai, Jun Hu, Quan Zhao et al.

In this paper, we present GRecX, an open-source TensorFlow framework for benchmarking GNN-based recommendation models in an efficient and unified way. GRecX consists of core libraries for building GNN-based recommendation benchmarks, as well as the implementations of popular GNN-based recommendation models. The core libraries provide essential components for building efficient and unified benchmarks, including FastMetrics (efficient metrics computation libraries), VectorSearch (efficient similarity search libraries for dense vectors), BatchEval (efficient mini-batch evaluation libraries), and DataManager (unified dataset management libraries). Especially, to provide a unified benchmark for the fair comparison of different complex GNN-based recommendation models, we design a new metric GRMF-X and integrate it into the FastMetrics component. Based on a TensorFlow GNN library tf_geometric, GRecX carefully implements a variety of popular GNN-based recommendation models. We carefully implement these baseline models to reproduce the performance reported in the literature, and our implementations are usually more efficient and friendly. In conclusion, GRecX enables uses to train and benchmark GNN-based recommendation baselines in an efficient and unified way. We conduct experiments with GRecX, and the experimental results show that GRecX allows us to train and benchmark GNN-based recommendation baselines in an efficient and unified way. The source code of GRecX is available at https://github.com/maenzhier/GRecX.

Jun Hu, Shengsheng Qian, Quan Fang et al.

We introduce tf_geometric, an efficient and friendly library for graph deep learning, which is compatible with both TensorFlow 1.x and 2.x. tf_geometric provides kernel libraries for building Graph Neural Networks (GNNs) as well as implementations of popular GNNs. The kernel libraries consist of infrastructures for building efficient GNNs, including graph data structures, graph map-reduce framework, graph mini-batch strategy, etc. These infrastructures enable tf_geometric to support single-graph computation, multi-graph computation, graph mini-batch, distributed training, etc.; therefore, tf_geometric can be used for a variety of graph deep learning tasks, such as transductive node classification, inductive node classification, link prediction, and graph classification. Based on the kernel libraries, tf_geometric implements a variety of popular GNN models for different tasks. To facilitate the implementation of GNNs, tf_geometric also provides some other libraries for dataset management, graph sampling, etc. Different from existing popular GNN libraries, tf_geometric provides not only Object-Oriented Programming (OOP) APIs, but also Functional APIs, which enable tf_geometric to handle advanced graph deep learning tasks such as graph meta-learning. The APIs of tf_geometric are friendly, and they are suitable for both beginners and experts. In this paper, we first present an overview of tf_geometric's framework. Then, we conduct experiments on some benchmark datasets and report the performance of several popular GNN models implemented by tf_geometric.

Weizhu Bao, Wei Jiang, Yan Wang et al.

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.