Related papers: Fast Parallel Randomized QR with Column Pivoting A…

The increasing size of transformer-based models in NLP makes the question of compressing them important. In this work, we present a comprehensive analysis of factorization based model compression techniques. Specifically, we focus on…

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its…

We present qrpca, a fast and scalable QR-decomposition principal component analysis package. The software, written in both R and python languages, makes use of torch for internal matrix computations, and enables GPU acceleration, when…

Repairing faulty quantum circuits is challenging and requires automated solutions. We present QRep, an automated repair approach that iteratively identifies and repairs faults in a circuit. QRep uniformly applies patches across the circuit…

While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute. For large matrix sizes, it is well known that the QR decomposition provides a tractable alternative. Under the assumption that it…

Traditional post-training quantization (PTQ) is considered an effective approach to reduce model size and accelerate inference of large-scale language models (LLMs). However, existing low-rank PTQ methods require costly fine-tuning to…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the…

In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…

Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…

Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging…

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…

The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at…

Randomized compiling (RC) is an efficient method for tailoring arbitrary Markovian errors into stochastic Pauli channels. However, the standard procedure for implementing the protocol in software comes with a large experimental overhead --…

Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not…

In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…

QMCPACK has enabled cutting-edge materials research on supercomputers for over a decade. It scales nearly ideally but has low single-node efficiency due to the physics-based abstractions using array-of-structures objects, causing…