Related papers: Degree reduction techniques for polynomial optimiz…

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

Large language models (LLMs) have transformed natural language processing but pose significant challenges for real-world deployment. These models necessitate considerable computing resources, which can be costly and frequently unavailable.…

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…

We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation).…

Reinforcement Learning (RL) has outperformed other counterparts in sequential decision-making and dynamic environment control. However, FPGA deployment is significantly resource-expensive, as associated with large number of computations in…

Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL's benefits…

Large Language Models (LLMs) have shown impressive capabilities in multi-step reasoning and problem-solving.Recent works introduce multi-agent reflection frameworks where multiple LLM agents critique and refine each other's outputs using…

Modular, distributed and multi-core architectures are currently considered a promising approach for scalability of quantum computing systems. The integration of multiple Quantum Processing Units necessitates classical and quantum-coherent…

Large-scale language models (LLMs) excel in language processing tasks but face deployment challenges due to high memory and computational demands. While low-bit quantization, such as 4-bit techniques, offers a potential solution, these…

We introduce a Reinforcement Learning (RL)-based method for re-synthesis of quantum circuits containing arbitrary Pauli rotations alongside Clifford operations. By collapsing each sub-block to a compact representation and then synthesizing…

We consider in this paper a class of semi-continuous quadratic programming problems which arises in many real-world applications such as production planning, portfolio selection and subset selection in regression. We propose a…

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these…

We present a reinforcement learning (RL)-driven framework for optimizing block-preconditioner sizes in iterative solvers used in portfolio optimization and option pricing. The covariance matrix in portfolio optimization or the…

Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple (lcm) of all the moduli can be accurately reconstructed when the number of…

Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…

In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…

We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…