Related papers: The Complex Gaussian Kernel LMS algorithm

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Knowledge graphs (KGs) are vital for knowledge-intensive tasks and have shown promise in reducing hallucinations in large language models (LLMs). However, constructing high-quality KGs remains difficult, requiring accurate information…

We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…

In recent years, there has been tremendous progress in the development of quantum computing hardware, algorithms and services leading to the expectation that in the near future quantum computers will be capable of performing simulations for…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

The advent of large scale, high-throughput genomic screening has introduced a wide range of tests for diagnostic purposes. Prominent among them are tests using miRNA expression levels. Genomics and proteomics now provide expression levels…

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation.…

This letter generalizes the Graph Signal Recovery (GSR) problem in Graph Signal Processing (GSP) to the Quaternion domain. It extends the Quaternion Least Mean Square (QLMS) in adaptive filtering literature, and Graph LMS (GLMS) algorithm…

Modern clustering approaches often trade interpretability for performance, particularly in deep learning-based methods. We present Generative Kernel Spectral Clustering (GenKSC), a novel model combining kernel spectral clustering with…

As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…

Large language model (LLM) inference poses significant challenges due to its intensive memory and computation demands. Weight and activation quantization (WAQ) offers a promising solution by reducing both memory footprint and arithmetic…

This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels…

This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…

Among various quantum machine learning (QML) algorithms, the quantum kernel method has especially attracted attention due to its compatibility with noisy intermediate-scale quantum devices and its potential to achieve quantum advantage.…

The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…

The performance of modern AI systems is fundamentally constrained by the quality of their underlying kernels, which translate high-level algorithmic semantics into low-level hardware operations. Achieving near-optimal kernels requires…