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The efficiency of Large Language Model~(LLM) inference is often constrained by substantial memory bandwidth and capacity demands. Existing techniques, such as pruning, quantization, and mixture of experts/depth, reduce memory capacity…
Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algorithms can drastically reduce the required computational…
The rapid expansion of computational capabilities and the ever-growing scale of modern HPC systems present formidable challenges in managing exascale scientific data. Faced with such vast datasets, traditional lossless compression…
Communication-avoiding Krylov methods require solving small dense Gram systems at each outer iteration. We present a low-synchronization approach based on Forward Gauss--Seidel (FGS), which exploits the structure of Gram matrices arising…
Driven by the insatiable needs to process ever larger amount of data with more complex models, modern computer processors and accelerators are beginning to offer half precision floating point arithmetic support, and extremely optimized…
3D Gaussian Splatting (3DGS) achieves impressive rendering fidelity and speed for novel view synthesis. However, its substantial data size poses a significant challenge for practical applications. While many compression techniques have been…
Predicting ground state energies of quantum many-body systems is one of the central computational challenges in quantum chemistry, physics, and materials science. Krylov subspace methods, such as Krylov Quantum Diagonalization and…
Huffman compression is a statistical, lossless, data compression algorithm that compresses data by assigning variable length codes to symbols, with the more frequently appearing symbols given shorter codes than the less. This work is a…
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…
Existing AI-based point cloud compression methods struggle with dependence on specific training data distributions, which limits their real-world deployment. Implicit Neural Representation (INR) methods solve the above problem by encoding…
We consider the problem of computing a QR (or QZ) decomposition of a real, dense, tall and very skinny matrix. That is, the number of columns is tiny compared to the number of rows, rendering most computations completely or partially…
Transformer-based Large Language Models (LLMs) have made a significant impact on various domains. However, LLMs' efficiency suffers from both heavy computation and memory overheads. Compression techniques like sparsification and…
We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weights. We propose two novel strategies combining Krylov…
As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…
This paper introduces HyperEF 2.0, a scalable framework for spectral coarsening and clustering of large-scale hypergraphs through hyperedge effective resistances, aiming to decompose hypergraphs into multiple node clusters with a small…
Gaussian Splatting (GS) has recently emerged as a state-of-the-art representation for radiance fields, combining real-time rendering with high visual fidelity. However, GS models require storing millions of parameters, leading to large file…
Implicit neural representations (INRs) have achieved remarkable success in image representation and compression, but they require substantial training time and memory. Meanwhile, recent 2D Gaussian Splatting (GS) methods (\textit{e.g.},…
In GPU-accelerated data analytics, the overhead of data transfer from CPU to GPU becomes a performance bottleneck when the data scales beyond GPU memory capacity due to the limited PCIe bandwidth. Data compression has come to rescue for…
Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…