8 papers
Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products
Soumyadip Ghosh, Lior Horesh, Vasileios Kalantzis +3
Counting triangles in graphs is a fundamental operation in network analysis, underpinning metrics such as clustering coefficients and serving as a signal for community detection, l…
Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules
Paulina Hoyos, Shashanka Ubaru, Dongsung Huh +5
Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error that compoun…
PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty
Paz Fink Shustin, Shashanka Ubaru, MaÅgorzata J. ZimoÅ +4
Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantificati…
Stable Iterative Solvers for Ill-conditioned Linear Systems
Vasileios Kalantzis, Mark S. Squillante, Chai Wah Wu
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicabilit…
Multi-Sense Embeddings for Language Models and Knowledge Distillation
Qitong Wang, Mohammed J. Zaki, Georgios Kollias +1
Transformer-based large language models (LLMs) rely on contextual embeddings which generate different (continuous) representations for the same token depending on its surrounding c…
Stable iterative refinement algorithms for solving linear systems
Chai Wah Wu, Mark S. Squillante, Vasileios Kalantzis +1
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed t…