Nonconvex Generalization of ADMM for Nonlinear Equality Constrained Problems

The ever-increasing demand for efficient and distributed optimization algorithms for large-scale data has led to the growing popularity of the Alternating Direction Method of Multipliers (ADMM). However, although the use of ADMM to solve linear equality constrained problems is well understood, we lacks a generic framework for solving problems with nonlinear equality constraints, which are common in practical applications (e.g., spherical constraints). To address this problem, we are proposing a new generic ADMM framework for handling nonlinear equality constraints, neADMM. After introducing the generalized problem formulation and the neADMM algorithm, the convergence properties of neADMM are discussed, along with its sublinear convergence rate $o(1/k)$, where $k$ is the number of iterations. Next, two important applications of neADMM are considered and the paper concludes by describing extensive experiments on several synthetic and real-world datasets to demonstrate the convergence and effectiveness of neADMM compared to existing state-of-the-art methods

Curriculum Learning for Graph Neural Networks: Which Edges Should We Learn First

Graph Neural Networks (GNNs) have achieved great success in representing data with dependencies by recursively propagating and aggregating messages along the edges. However, edges in real-world graphs often have varying degrees of difficulty, and some edges may even be noisy to the downstream tasks. Therefore, existing GNNs may lead to suboptimal learned representations because they usually treat every edge in the graph equally. On the other hand, Curriculum Learning (CL), which mimics the human learning principle of learning data samples in a meaningful order, has been shown to be effective in improving the generalization ability and robustness of representation learners by gradually proceeding from easy to more difficult samples during training. Unfortunately, existing CL strategies are designed for independent data samples and cannot trivially generalize to handle data dependencies. To address these issues, we propose a novel CL strategy to gradually incorporate more edges into training according to their difficulty from easy to hard, where the degree of difficulty is measured by how well the edges are expected given the model training status. We demonstrate the strength of our proposed method in improving the generalization ability and robustness of learned representations through extensive experiments on nine synthetic datasets and nine real-world datasets. The code for our proposed method is available at https://github.com/rollingstonezz/Curriculum_learning_for_GNNs.Comment: Accepted by NeurIPS 202

Degenerate lower dimensional tori in reversible systems

AbstractIn this paper we prove the persistence of lower dimensional invariant tori with prescribed frequencies and singular normal matrices in reversible systems. The normal variable is two-dimensional and the unperturbed nonlinear terms in the differential equation for this variable have a special structure

Method for robotic motion compensation during PET imaging of mobile subjects

Studies of the human brain during natural activities, such as locomotion, would benefit from the ability to image deep brain structures during these activities. While Positron Emission Tomography (PET) can image these structures, the bulk and weight of current scanners are not compatible with the desire for a wearable device. This has motivated the design of a robotic system to support a PET imaging system around the subject's head and to move the system to accommodate natural motion. We report here the design and experimental evaluation of a prototype robotic system that senses motion of a subject's head, using parallel string encoders connected between the robot-supported imaging ring and a helmet worn by the subject. This measurement is used to robotically move the imaging ring (coarse motion correction) and to compensate for residual motion during image reconstruction (fine motion correction). Minimization of latency and measurement error are the key design goals, respectively, for coarse and fine motion correction. The system is evaluated using recorded human head motions during locomotion, with a mock imaging system consisting of lasers and cameras, and is shown to provide an overall system latency of about 80 ms, which is sufficient for coarse motion correction and collision avoidance, as well as a measurement accuracy of about 0.5 mm for fine motion correction.Comment: 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

A Novel Scholar Embedding Model for Interdisciplinary Collaboration

Interdisciplinary collaboration has become a driving force for scientific breakthroughs, and evaluating scholars' performance in interdisciplinary researches is essential for promoting such collaborations.However, traditional scholar evaluation methods based solely on individual achievements do not consider interdisciplinary cooperation, creating a challenge for interdisciplinary scholar evaluation and recommendation. To address this issue, we propose a scholar embedding model that quantifies and represents scholars based on global semantic information and social influence, enabling real-time tracking of scholars' research trends. Our model incorporates semantic information and social influence for interdisciplinary scholar evaluation, laying the foundation for future interdisciplinary collaboration discovery and recommendation projects. We demonstrate the effectiveness of our model on a sample of scholars from the Beijing University of Posts and Telecommunications.Comment: 9 pages, 4 figures, 1 tabl