Related papers: Giga-scale Kernel Matrix Vector Multiplication on …
Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$…
Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive…
Quantum circuit mapping is a critical process in quantum computing that involves adapting logical quantum circuits to adhere to hardware constraints, thereby generating physically executable quantum circuits. Current quantum circuit mapping…
K-means is a popular clustering algorithm with significant applications in numerous scientific and engineering areas. One drawback of K-means is its inability to identify non-linearly separable clusters, which may lead to inaccurate…
Quantization has emerged to be an effective way to significantly boost the performance of deep neural networks (DNNs) by utilizing low-bit computations. Despite having lower numerical precision, quantized DNNs are able to reduce both memory…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
Large Language Models (LLMs) face significant deployment challenges due to their substantial resource requirements. While low-bit quantized weights can reduce memory usage and improve inference efficiency, current hardware lacks native…
Large language models (LLMs) have grown beyond the memory capacity of single GPU devices, necessitating quantization techniques for practical deployment. While NF4 (4-bit NormalFloat) quantization enables 4$\times$ memory reduction,…
In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our…
We describe an interface and an implementation for performing Kronecker product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays processed in parallel as a batch. This method is suited to cases where the Kronecker…
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
Bayesian inference for exponential family random graph models (ERGMs) is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo…
An infinitely wide model is a weighted integration $\int \varphi(x,v) d \mu(v)$ of feature maps. This model excels at handling an infinite number of features, and thus it has been adopted to the theoretical study of deep learning. Kernel…
This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware…
Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles…
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data,…
Infinite width limit has shed light on generalization and optimization aspects of deep learning by establishing connections between neural networks and kernel methods. Despite their importance, the utility of these kernel methods was…
Sparse General Matrix-Matrix Multiplication (SpGEMM) is a fundamental operation in numerous scientific computing and data analytics applications, often bottlenecked by irregular memory access patterns. This paper presents Hash based…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…