Related papers: Permutation of Tensor-Train Cores for Computing Mo…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a…
Dynamic graph learning is essential for applications involving temporal networks and requires effective modeling of temporal relationships. Seminal attention-based models like TGAT and DyGFormer rely on sinusoidal time encoders to capture…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
The development of cluster computing frameworks has allowed practitioners to scale out various statistical estimation and machine learning algorithms with minimal programming effort. This is especially true for machine learning problems…
Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
Learning from spatio-temporal data has numerous applications such as human-behavior analysis, object tracking, video compression, and physics simulation.However, existing methods still perform poorly on challenging video tasks such as…
Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…
The directional state transition tensor (DSTT) reduces the complexity of state transition tensor (STT) by aligning the STT terms in sensitive directions only, which provides comparable accuracy in orbital uncertainty propagation. The DSTT…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a…
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…
The rapid growth of streaming media and e-commerce has driven advancements in recommendation systems, particularly Sequential Recommendation Systems (SRS). These systems employ users' interaction histories to predict future preferences.…
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…