Initialization Method for Factorization Machine Based on Low-Rank Approximation for Constructing a Corrected Approximate Ising Model
This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM is applied to black-box combinatorial optimization problems using factorization machine with quantum annealing (FMQA). It is anticipated that the optimization performance of FMQA will be enhanced through an implementation of the warm-start method. Nevertheless, the optimal initialization method for leveraging the warm-start approach in FMQA remains undetermined. Consequently, the present study compares initialization methods based on random initialization and low-rank approximation, and then identifies a suitable one for use with warm-start in FMQA through numerical experiments. Furthermore, the properties of the initialization method by the low-rank approximation for the FM are analyzed using random matrix theory, demonstrating that the approximation accuracy of the proposed method is not significantly influenced by the specific Ising model under consideration. The findings of this study will facilitate advancements of research in the field of black-box combinatorial optimization through the use of Ising machines.
Code (0)
등록된 구현이 없습니다.
Tasks
Combinatorial OptimizationSimilar Papers 제목 키워드 기반
Algorithmic Regularization in Model-free Overparametrized Asymmetric Matrix Factorization
We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values …
Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization
Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that…
Efficient Wireless Federated Learning via Low-Rank Gradient Factorization
This paper presents a novel gradient compression method for federated learning (FL) in wireless systems. The proposed method centers on a low-rank matrix factorization strategy for local gradient compression that is base…
Federated LearningLow-rank compressionImproved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correction
Due to the iterative nature of most nonnegative matrix factorization (\textsc{NMF}) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many ini…
Understanding Incremental Learning with Closed-form Solution to Gradient Flow on Overparamerterized Matrix Factorization
Many theoretical studies on neural networks attribute their excellent empirical performance to the implicit bias or regularization induced by first-order optimization algorithms when training networks under certain initi…
Incremental Learning