Related papers: The Divide-and-Conquer Framework: A Suitable Setti…
Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful…
We present an efficient task and motion replanning approach for sequential multi-object manipulation in dynamic environments. Conventional Task And Motion Planning (TAMP) solvers experience an exponential increase in planning time as the…
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…
Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
For dense Hermitian matrices with small off-diagonal (numerical) ranks and in a hierarchically semiseparable form, we give a stable divide-and-conquer eigendecomposition method with nearly linear complexity (called SuperDC) that…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities,…
Large language models (LLMs) have demonstrated strong reasoning capabilities through step-by-step chain-of-thought (CoT) reasoning. Nevertheless, at the limits of model capability, CoT often proves insufficient, and its strictly sequential…
Resource-constrained robots often suffer from energy inefficiencies, underutilized computational abilities due to inadequate task allocation, and a lack of robustness in dynamic environments, all of which strongly affect their performance.…
There is growing interest in object detection in advanced driver assistance systems and autonomous robots and vehicles. To enable such innovative systems, we need faster object detection. In this work, we investigate the trade-off between…
Memory-Bounded Dynamic Programming (MBDP) has proved extremely effective in solving decentralized POMDPs with large horizons. We generalize the algorithm and improve its scalability by reducing the complexity with respect to the number of…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
The future of computing systems is inevitably embracing a disaggregated and composable pattern: from clusters of computers to pools of resources that can be dynamically combined together and tailored around applications requirements.…