# Subsampling Factorization Machine Annealing

arXiv: https://arxiv.org/abs/2508.08778 · HTML: https://mlsanity.com/paper/2508.08778/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 106 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimisation](https://mlsanity.com/paper/2402.03990/) (2024)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming](https://mlsanity.com/paper/2204.10579/) (2022)
- [Lossy compression of statistical data using quantum annealer](https://mlsanity.com/paper/2110.02142/) (2021)
- [Implementation of Trained Factorization Machine Recommendation System on Quantum Annealer](https://mlsanity.com/paper/2210.12953/) (2022)
- [A black-box optimization method with polynomial-based kernels and quadratic-optimization annealing](https://mlsanity.com/paper/2501.04225/) (2025)
- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)
- [Image Analysis Based on Nonnegative/Binary Matrix Factorization](https://mlsanity.com/paper/2007.00889/) (2020)
- [Quantum Approximate Bayesian Optimization Algorithms with Two Mixers and Uncertainty Quantification](https://mlsanity.com/paper/2307.16335/) (2023)
- [Random Postprocessing for Combinatorial Bayesian Optimization](https://mlsanity.com/paper/2309.02842/) (2023)
- [Real-Time Black-Box Optimization for Dynamic Discrete Environments Using Embedded Ising Machines](https://mlsanity.com/paper/2506.16924/) (2025)
- [CRYSIM: Prediction of Symmetric Structures of Large Crystals with GPU-based Ising Machines](https://mlsanity.com/paper/2504.06878/) (2025)

## Built on by (most cited first, 1 of 1)

- [Stage-dependent integer-binary encoding in factorization-machine black-box optimization](https://mlsanity.com/paper/2606.23188/) (2026)

## Abstract (arXiv)

Quantum computing and machine learning are state-of-the-art technologies that have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve complex problems in many branches of science and engineering such as combinatorial optimization problems and accelerate the creation of next-generation technologies. In this work, we develop an algorithm to solve a black-box optimization problem by improving Factorization Machine Annealing (FMA) such that the training of a machine learning model called Factorization Machine is performed not by a full dataset but by a subdataset that is sampled from a full dataset: Subsampling Factorization Machine Annealing (SFMA). According to such a probabilistic training process, the performance of FMA on exploring a solution space gets enhanced. As a result, SFMA exhibits balanced performance of exploration and exploitation, which we call exploitation-exploration functionality. We conduct numerical benchmarking tests to compare the performance of SFMA with that of FMA. Consequently, SFMA certainly exhibits the exploration-exploitation functionality and outperforms FMA in speed and accuracy. In addition, the performance of SFMA can be further improved by sequentially using two subsampling datasets with different sizes such that the size of the latter dataset is substantially smaller than the former. Such a substantial reduction not only enhances the exploration performance of SFMA but also enables us to run it with correspondingly low computational cost even for a large-scale problem. These results indicate the effectiveness of SFMA in a certain class of black-box optimization problems of significant size: the potential scalability of SFMA in solving large-scale problems with correspondingly low computational cost.