Computing distances on Riemannian manifolds is a challenging problem with numerous applications, from physics, through statistics, to machine learning. In this paper, we introduce the metric-constrained Eikonal solver to obtain continuous, differentiable representations of distance functions on manifolds. The differentiable nature of these representations allows for the direct computation of globally length-minimising paths on the manifold. We showcase the use of metric-constrained Eikonal solvers for a range of manifolds and demonstrate the applications. First, we demonstrate that metric-constrained Eikonal solvers can be used to obtain the Fréchet mean on a manifold, employing the definition of a Gaussian mixture model, which has an analytical solution to verify the numerical results. Second, we demonstrate how the obtained distance function can be used to conduct unsupervised clustering on the manifold -- a task for which existing approaches are computationally prohibitive. This work opens opportunities for distance computations on manifolds.
Revenue and Energy Efficiency-Driven Delay Constrained Computing Task Offloading and Resource Allocation in a Vehicular Edge Computing Network: A Deep Reinforcement Learning Approach
Secure Resource Allocation via Constrained Deep Reinforcement Learning
School of Computing & Information Systems, Singapore Management University（新加坡管理大学计算与信息系统学院）；School of Computing & Artificial Intelligence, Southwestern University of Finance and Economics（西南财经大学计算机与人工智能学院）；College of Computing & Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Memory- and Latency-Constrained Inference of Large Language Models via Adaptive Split Computing
Department of Artificial Intelligence, Kyungpook National University（人工智能系，庆北国立大学）；Department of Electrical and Computer Engineering, Queen’s University（电气与计算机工程系，皇后大学）；Department of Information and Communications Engineering, Pukyong National University（信息与通信工程系，浦项国立大学）
aphBO-2GP-3B: A budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture
Sandia National Laboratories（桑迪亚国家实验室）；Xilinx Inc.（赛灵思公司）；Medpace Inc.（Medpace公司）；GIW Industries Inc.（GIW工业公司）
Adaptive Federated Learning in Resource Constrained Edge Computing Systems
IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Imperial College London（帝国理工学院）；Pennsylvania State University（宾夕法尼亚州立大学）；Army Research Laboratory（陆军研究实验室）
Data-Aware Gradient Compression for FL in Communication-Constrained Mobile Computing
Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；AI Cloud Business Group, Baidu Incorporated（百度公司AI云业务集团）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；Department of Computer Science and Technology, Harbin Institute of Technology（哈尔滨工业大学计算机科学与技术系）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）
Quantum Algorithms for solving Hard Constrained Optimisation Problems
La Salle - Ramon Llull University（拉蒙柳尔大学拉萨尔学院）；IBMQ（IBM量子）；AWS-Braket（AWS布拉凯特）
本文研究了求解硬约束优化问题的量子算法。它展示了量子计算机如何解决困难的日常问题，例如为社会工作者找到最佳时间表或机器人在仓库中挑选和整理的路径。解决方案的路径导致了一种新的人工智能范式的定义，包括量子计算，量子基于案例推理（qCBR），以及使用Raspberry Pi 4作为处理器（qRobot）将量子计算的能力集成到移动机器人中的概念验证，能够与IBMQ，Amazon Braket（D-Wave）和Pennylane等领先的技术参与者一起运行。为了提高变分算法在这个NISQ时代和下一个时代的执行时间，我们提出了EVA：一种量子指数值近似算法，它可以加速VQE，也就是说，到目前为止，量子计算的旗舰。为了提高变分算法在这个NISQ时代和下一个时代的执行时间，我们提出了EVA：一种量子指数值近似算法，它可以加速VQE，也就是说，到目前为止，量子计算的旗舰。
SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
Institute for Numerical Simulation, University of Bonn（数值模拟研究所，波恩大学）；Centre Borelli, ENS Paris-Saclay（博雷利中心，巴黎-萨克雷大学）；Institute for Applied Mathematics, University of Bonn（应用数学研究所，波恩大学）；Technion - Israel Institute of Technology（技术学院-以色列理工学院）
