Related papers: Efficient QR-Based CP Decomposition Acceleration v…

In this paper, the performance of quadratic residue (QR) codes of lengths within 100 is given and analyzed when the hard decoding, soft decoding, and linear programming decoding algorithms are utilized. We develop a simple method to…

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…

In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…

We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…

The ParaTuck-2 decomposition (PT2D) of third-order tensor is a two-layer generalization of the well-known canonical polyadic decomposition (CPD).While being more flexible than the CPD, the PT2D also possesses similar uniqueness…

In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…

This paper proposes a channel estimation method for Multiple-Input Multiple-Output (MIMO) systems based on Canonical Polyadic (CP) decomposition applied to a mode-factorized tensor representation of the channel. The proposed approach…

This paper initiates a series of studies on a COS-tensor framework, as an efficient alternative to MC for large and liquid portfolios characterized by a modest number of dominant risk factors but a large number of trades. The framework is…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

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…

The Pauli matrices are 2-by-2 matrices that are very useful in quantum computing. They can be used as elementary gates in quantum circuits but also to decompose any matrix of $\mathbb{C}^{2^n \times 2^n}$ as a linear combination of tensor…

This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows:…

This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization…

Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Tsigaridas for symmetric tensor canonical polyadic (CP)…

We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…