Related papers: hm-toolbox: Matlab software for HODLR and HSS matr…
Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this…
Large language model (LLM) routing aims to exploit the specialized strengths of different LLMs for diverse tasks. However, existing approaches typically focus on selecting LLM architectures while overlooking parameter settings, which are…
Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of…
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…
Structured dense matrices result from boundary integral problems in electrostatics and geostatistics, and also Schur complements in sparse preconditioners such as multi-frontal methods. Exploiting the structure of such matrices can reduce…
Visual Simultaneous Localization and Mapping (VSLAM) research faces significant challenges due to fragmented toolchains, complex system configurations, and inconsistent evaluation methodologies. To address these issues, we present…
Dynamic programming (DP) based algorithms are essential yet compute-intensive parts of numerous bioinformatics pipelines, which typically involve populating a 2-D scoring matrix based on a recursive formula, optionally followed by a…
High-level synthesis (HLS) allows hardware designers to create hardware designs with high-level programming languages like C/C++/OpenCL, which greatly improves hardware design productivity. However, existing HLS flows require programmers'…
Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…
Dataflow architectures are growing in popularity due to their potential to mitigate the challenges posed by the memory wall inherent to the Von Neumann architecture. At the same time, high-level synthesis (HLS) has demonstrated its efficacy…
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…
Training Long-Context Large Language Models (LLMs) is challenging, as hybrid training with long-context and short-context data often leads to workload imbalances. Existing works mainly use data packing to alleviate this issue, but fail to…
Large language models (LLMs) have significantly advanced natural language processing, particularly through the integration of external tools and APIs. However, their effectiveness is frequently hampered by parameter mis-filling during tool…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Hierarchical reinforcement learning methods offer a powerful means of planning flexible behavior in complicated domains. However, learning an appropriate hierarchical decomposition of a domain into subtasks remains a substantial challenge.…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new…