Related papers: Fast Data-independent KLT Approximations Based on …

Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…

Matrix approximation methods have successfully produced efficient, low-complexity approximate transforms for the discrete cosine transforms and the discrete Fourier transforms. For the DFT case, literature archives approximations operating…

Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT) and Discrete Cosine Transform (DCT) have been widely used as feature extractors in image processing but rarely applied in neural networks. However, we found that…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…

Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1)…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to improve running time and reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work…

This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…

This paper proposes a neural rendering approach that represents a scene as "compressed light-field tokens (CLiFTs)", retaining rich appearance and geometric information of a scene. CLiFT enables compute-efficient rendering by compressed…

In our previous work [arXiv:2202.10042], the complexity of Sinkhorn iteration is reduced from $O(N^2)$ to the optimal $O(N)$ by leveraging the special structure of the kernel matrix. In this paper, we explore the special structure of kernel…

We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the…

Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical…

Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size n limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with O(n log n)…

The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

Starlight subtraction algorithms based on the method of Karhunen-Lo\`eve eigenimages have proved invaluable to exoplanet direct imaging. However, they scale poorly in runtime when paired with differential imaging techniques. In such…

In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and without oversampling operation is developed. This DLCT is based on the well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp multiplications…

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient…

Cropping high-resolution document images into multiple sub-images is the most widely used approach for current Multimodal Large Language Models (MLLMs) to do document understanding. Most of current document understanding methods preserve…