相关论文: Complex-to-Real Sketches for Tensor Products with …

Power iteration can improve the accuracy of randomized SVD, but requires multiple data passes, making it impractical in streaming or memory-constrained settings. We introduce a lightweight yet effective sketch-power iteration, allowing…

As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference…

Compressive learning is an emerging approach to drastically reduce the memory footprint of large-scale learning, by first summarizing a large dataset into a low-dimensional sketch vector, and then decoding from this sketch the latent…

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the…

We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…

Compressive learning is an approach to efficient large scale learning based on sketching an entire dataset to a single mean embedding (the sketch), i.e. a vector of generalized moments. The learning task is then approximately solved as an…

We construct a matrix $M\in R^{m\otimes d^c}$ with just $m=O(c\,\lambda\,\varepsilon^{-2}\text{poly}\log1/\varepsilon\delta)$ rows, which preserves the norm $\|Mx\|_2=(1\pm\varepsilon)\|x\|_2$ of all $x$ in any given $\lambda$ dimensional…

Kernel density estimation is a simple and effective method that lies at the heart of many important machine learning applications. Unfortunately, kernel methods scale poorly for large, high dimensional datasets. Approximate kernel density…

The semi-tensor product of vectors generalizes the conventional inner product, enabling algebraic operations between vectors of different dimensions. Building upon this foundation, we introduce a domain-based convolutional product and…

Recent deep image-to-image translation techniques allow fast generation of face images from freehand sketches. However, existing solutions tend to overfit to sketches, thus requiring professional sketches or even edge maps as input. To…

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…

The quadratic time and memory complexity inherent to self-attention mechanisms, with respect to sequence length, presents a critical computational bottleneck in the training and deployment of large-scale Transformer-based language models.…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…

One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

Creating realistic virtual assets is a time-consuming process: it usually involves an artist designing the object, then spending a lot of effort on tweaking its appearance. Intricate details and certain effects, such as subsurface…

In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…