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Quadratic approximations form a fundamental building block of machine learning methods. E.g., second-order optimizers try to find the Newton step into the minimum of a local quadratic proxy to the objective function; and the second-order…
We use a numerical algorithm on the Lie group of rotation matrices to obtain rotated constellations for Rayleigh fading channels. Our approach minimizes the union bound for the pairwise error probability to produce rotations optimized for a…
In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard…
Binary codes can be used to speed up nearest neighbor search tasks in large scale data sets as they are efficient for both storage and retrieval. In this paper, we propose a robust auto-encoder model that preserves the geometric…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
Hashing is widely applied to approximate nearest neighbor search for large-scale multimodal retrieval with storage and computation efficiency. Cross-modal hashing improves the quality of hash coding by exploiting semantic correlations…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows…
This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…
We develop hierarchically quantized efficient embedding representations for similarity-based search and show that this representation provides not only the state of the art performance on the search accuracy but also provides several orders…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
Space-filling designs such as scrambled-Hammersley, Latin Hypercube Sampling and Jittered Sampling have been proposed for fully parallel hyperparameter search, and were shown to be more effective than random or grid search. In this paper,…
Near-term quantum computations are limited by high error rates, the scarcity of qubits and low qubit connectivity. Increasing support for mid-circuit measurements and qubit reset in near-term quantum computers enables qubit reuse that may…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity represented by a basis state in the…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…