Related papers: Dimension reduction with structure-aware quantum c…
This is a further development of Vision Transformer Pruning via matrix decomposition. The purpose of the Vision Transformer Pruning is to prune the dimension of the linear projection of the dataset by learning their associated importance…
With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…
A variation of the classic vector quantization problem is considered, in which the analog-to-digital (A2D) conversion is not constrained by the cardinality of the output but rather by the number of comparators available for quantization.…
Vector Quantization (VQ) is a widely used technique in machine learning and data compression, valued for its simplicity and interpretability. Among hard VQ methods, $k$-medoids clustering and Kernel Density Estimation (KDE) approaches…
Embedding methods such as word embedding have become pillars for many applications containing discrete structures. Conventional embedding methods directly associate each symbol with a continuous embedding vector, which is equivalent to…
In this paper, classical and continuous variable (CV) quantum neural network hybrid multiclassifiers are presented using the MNIST dataset. The combination of cutoff dimension and probability measurement method in the CV model allows a…
In order to leverage quantum computers for machine learning tasks such as image classification, careful consideration is required: NISQ-era quantum computers have limitations, which include noise, scalability, read-in and read-out times,…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…
We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…
In this paper, we present a class of high order methods to approximate the singular value decomposition of a given complex matrix (SVD). To the best of our knowledge, only methods up to order three appear in the the literature. A first part…
Word embedding is a useful approach to capture co-occurrence structures in large text corpora. However, in addition to the text data itself, we often have additional covariates associated with individual corpus documents---e.g. the…
The capacity of a learning machine is measured by its Vapnik-Chervonenkis dimension, and learning machines with a low VC dimension generalize better. It is well known that the VC dimension of SVMs can be very large or unbounded, even though…
Support vector machines (SVMs) have been successful in solving many computer vision tasks including image and video category recognition especially for small and mid-scale training problems. The principle of these non-parametric models is…
Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…
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…
In this paper a variation of the classic vector quantization problem is considered. In the standard formulation, a quantizer is designed to minimize the distortion between input and output when the number of reconstruction points is fixed.…
Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…
We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each…