Related papers: Upgrading Subgroup Triple Product Property Triples

Quantum optimal control plays a crucial role in the development of quantum technologies, particularly in the design and implementation of fast and accurate gates for quantum computing. Here, we present a method to synthesize gates using the…

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

With the latest advances in Deep Learning-based generative models, it has not taken long to take advantage of their remarkable performance in the area of time series. Deep neural networks used to work with time series heavily depend on the…

We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…

While tabular data is fundamental to many real-world machine learning (ML) applications, acquiring high-quality tabular data is usually labor-intensive and expensive. Limited by the scarcity of observations, tabular datasets often exhibit…

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…

Reinforcement learning algorithms such as group-relative policy optimization (GRPO) have shown strong potential for improving the mathematical reasoning capabilities of large language models. While a growing body of work seeks to improve…

Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG)…

Model merging is to combine fine-tuned models derived from multiple domains, with the intent of enhancing the model's proficiency across various domains. The principal concern is the resolution of parameter conflicts. A substantial amount…

The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…

We propose Newton-PIPG, an efficient method for solving quadratic programming (QP) problems arising in optimal control, subject to additional set constraints. Newton-PIPG integrates the Proportional-Integral Projected Gradient (PIPG) method…

A multitude of industries depend on accurate and reasonable tabular data augmentation for their business processes. Contemporary methodologies in generating tabular data revolve around utilizing Generative Adversarial Networks (GAN) or…

A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be…

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…

Deep learning and especially the use of Deep Neural Networks (DNNs) provides impressive results in various regression and classification tasks. However, to achieve these results, there is a high demand for computing and storing resources.…

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

Chain-of-Thought (CoT) prompting methods have enabled large language models (LLMs) to generate reasoning paths and solve math word problems (MWPs). However, they are sensitive to mistakes in the paths, as any mistake can result in an…