相关论文: What if Neural Networks had SVDs?

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

A key characteristic of work on deep learning and neural networks in general is that it relies on representations of the input that support generalization, robust inference, domain adaptation and other desirable functionalities. Much recent…

Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…

This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs that have substantially impacted the computer vision community. Unlike previous methods that are designed for…

Convolutional neural networks have enabled accurate image super-resolution in real-time. However, recent attempts to benefit from temporal correlations in video super-resolution have been limited to naive or inefficient architectures. In…

Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…

We consider the problem of updating the SVD when augmenting a "tall thin" matrix, i.e., a rectangular matrix $A \in \RR^{m \times n}$ with $m \gg n$. Supposing that an SVD of $A$ is already known, and given a matrix $B \in \RR^{m \times…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

Artificial Neural Networks (ANNs) have received increasing attention in recent years with applications that span a wide range of disciplines including vital domains such as medicine, network security and autonomous transportation. However,…

This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the…

The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank…

The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…

We propose multirate training of neural networks: partitioning neural network parameters into "fast" and "slow" parts which are trained on different time scales, where slow parts are updated less frequently. By choosing appropriate…

Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…

Singular Value Decomposition (SVD) is a fundamental matrix factorization technique in linear algebra, widely applied in numerous matrix-related problems. However, traditional SVD approaches are hindered by slow panel factorization and…

The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…

Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…

Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…

Singular value decomposition (SVD) is widely used for dimensionality reduction and noise suppression, and it plays a pivotal role in numerous scientific and engineering applications. As the dimensions of the matrix grow rapidly, the…