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arxiv: 2507.18003 · v1 · submitted 2025-07-24 · ❄️ cond-mat.stat-mech · quant-ph

Black-box optimization using factorization and Ising machines

Ryo Tamura , Yuya Seki , Yuki Minamoto , Koki Kitai , Yoshiki Matsuda , Shu Tanaka , Koji Tsuda This is my paper

Pith reviewed 2026-05-19 03:25 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords black-box optimizationfactorization machineIsing machinequadratic unconstrained binary optimizationquantum annealingsurrogate modelacquisition functionBayesian optimization
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The pith

A factorization machine surrogate converts black-box optimization into a quadratic binary problem solvable by Ising machines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review describes the FMQA algorithm for black-box optimization in materials design, drug discovery, and hyperparameter tuning. A factorization machine acts as the surrogate model and converts directly into a quadratic unconstrained binary optimization form. Ising machines then solve the acquisition-function step that is otherwise difficult with conventional solvers. The resulting workflow scales to larger problems and comes with Python packages for immediate use. The paper surveys successful applications to binary, integer, graph, and string problems across physics, chemistry, materials science, and social sciences.

Core claim

The FMQA algorithm realizes fast computations of black-box optimization using Ising machines by using a factorization machine as a surrogate model that can be directly transformed into a quadratic unconstrained binary optimization model solved on the machine to locate the next evaluation point.

What carries the argument

Factorization machine surrogate model that maps directly to a quadratic unconstrained binary optimization problem for acquisition-function optimization on Ising machines.

If this is right

  • Large-scale black-box problems become tractable because the acquisition step runs on Ising hardware instead of classical solvers.
  • The same workflow applies to binary and integer variables as well as graph, network, and string representations via a binary variational autoencoder.
  • Python packages allow direct implementation without additional surrogate-to-QUBO conversion code.
  • Applications already span physics, chemistry, materials science, and social-science domains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the factorization-machine mapping remains faithful for higher-dimensional inputs, the method could extend Bayesian optimization to domains where classical acquisition maximization currently dominates runtime.
  • Hybrid classical-quantum solvers might relax the binary-variable restriction and allow direct handling of continuous black-box problems.
  • Replacing or augmenting the factorization machine with other sparse surrogate architectures could improve accuracy on strongly nonlinear objectives while retaining the QUBO conversion step.

Load-bearing premise

The factorization machine surrogate must capture the black-box function's behavior well enough to produce useful acquisition-function optima at the problem sizes examined.

What would settle it

On a high-dimensional benchmark black-box function, compare the number of evaluations needed by FMQA versus standard Bayesian optimization with Gaussian-process surrogates to reach a target objective value; a clear slowdown or failure to improve would disprove the scaling advantage.

Figures

Figures reproduced from arXiv: 2507.18003 by Koji Tsuda, Koki Kitai, Ryo Tamura, Shu Tanaka, Yoshiki Matsuda, Yuki Minamoto, Yuya Seki.

Figure 1
Figure 1. Figure 1: FIG. 1. Flow of the FMQA algorithm that performs BBO using FM [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Three types of optimization problems depending on the type [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Optimization target of metamaterial structure constructed by three types rod-like materials (SiO [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Triblock polymers defined by 15 bits. (b) Cycle dependence of the best TC for 20 independent runs. (c) Example of conductive [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Structure of MgGa [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Cycle dependence of the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Target topological shape of the thermal radiator for the thermal emitter design. (b) Cycle dependence on efficiencies by FMQA. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Black-box optimization (BBO) is used in materials design, drug discovery, and hyperparameter tuning in machine learning. The world is experiencing several of these problems. In this review, a factorization machine with quantum annealing or with quadratic-optimization annealing (FMQA) algorithm to realize fast computations of BBO using Ising machines (IMs) is discussed. The FMQA algorithm uses a factorization machine (FM) as a surrogate model for BBO. The FM model can be directly transformed into a quadratic unconstrained binary optimization model that can be solved using IMs. This makes it possible to optimize the acquisition function in BBO, which is a difficult task using conventional methods without IMs. Consequently, it has the advantage of handling large BBO problems. To be able to perform BBO with the FMQA algorithm immediately, we introduce the FMQA algorithm along with Python packages to run it. In addition, we review examples of applications of the FMQA algorithm in various fields, including physics, chemistry, materials science, and social sciences. These successful examples include binary and integer optimization problems, as well as more general optimization problems involving graphs, networks, and strings, using a binary variational autoencoder. We believe that BBO using the FMQA algorithm will become a key technology in IMs including quantum annealers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reviews the FMQA algorithm for black-box optimization, in which a factorization machine serves as a surrogate model that is directly mapped to a QUBO form solvable by Ising machines. This mapping is presented as enabling efficient acquisition-function optimization for large-scale BBO problems in materials design, drug discovery, and related domains. The text introduces the algorithm together with Python packages for immediate use and surveys prior applications across physics, chemistry, materials science, and social sciences, including binary/integer problems as well as graph, network, and string optimizations realized via binary variational autoencoders.

Significance. If the reviewed FM-to-QUBO mapping and surrogate accuracy hold at the scales claimed, the work could provide a practical bridge between established surrogate-based BBO and emerging Ising-machine hardware, offering a route to faster acquisition optimization than conventional methods. The inclusion of ready-to-use code and concrete application examples adds immediate utility for experimental and computational researchers.

major comments (1)
  1. [Abstract] Abstract and introductory sections: the central assertion that FMQA 'has the advantage of handling large BBO problems' rests on the premise that the FM surrogate remains sufficiently accurate to guide acquisition optimization. The manuscript reviews prior successes but supplies no new scaling analysis, surrogate-error bounds, or ablation against higher-order models that would confirm the pairwise-interaction approximation does not degrade for the higher-dimensional or non-additive objectives typical in the cited domains.
minor comments (2)
  1. A summary table listing the reviewed applications, problem dimensionality, number of black-box evaluations, and reported performance gains relative to baselines would improve readability and allow readers to assess the practical reach of the method.
  2. The description of the FM-to-QUBO transformation would benefit from an explicit equation or short pseudocode block showing how the factorization-machine parameters enter the quadratic terms, even if the mapping is standard.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our review manuscript and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introductory sections: the central assertion that FMQA 'has the advantage of handling large BBO problems' rests on the premise that the FM surrogate remains sufficiently accurate to guide acquisition optimization. The manuscript reviews prior successes but supplies no new scaling analysis, surrogate-error bounds, or ablation against higher-order models that would confirm the pairwise-interaction approximation does not degrade for the higher-dimensional or non-additive objectives typical in the cited domains.

    Authors: We appreciate this observation. The manuscript is a review of the FMQA algorithm and its applications; the statement regarding large-scale BBO problems summarizes empirical results from the cited literature rather than presenting new theoretical guarantees. Those prior studies include successful applications to high-dimensional problems in materials science and drug discovery. As a review we do not introduce new scaling analyses or ablations. We will, however, revise the abstract and introduction to qualify the claim more explicitly by pointing to the specific empirical evidence in the surveyed works and add a concise paragraph in the discussion section on the known limitations of the pairwise FM approximation, including references to cases where higher-order interactions may become relevant. revision: partial

Circularity Check

0 steps flagged

No circularity: review of established FM-to-QUBO mapping for BBO

full rationale

The manuscript is explicitly a review of the FMQA algorithm, which uses a factorization machine surrogate that maps directly to a QUBO solvable by Ising machines. No new derivation chain is presented; the central transformation is described as a standard property of factorization machines rather than derived from quantities defined in terms of the paper's own fitted parameters or self-citations. The text focuses on implementation, Python packages, and prior applications across fields without claiming predictions that reduce by construction to inputs. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The review rests on the domain assumption that factorization machines provide usable surrogates for black-box functions and that Ising machines can solve the resulting QUBO instances efficiently.

axioms (1)
  • domain assumption Factorization machines serve as effective surrogate models for black-box optimization functions.
    Central to transforming the surrogate into a QUBO solvable by Ising machines.

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Forward citations

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Two decades of blackbox optimization applications,

    pp. 1487–1495. 2S. Alarie, C. Audet, A. E. Gheribi, M. Kokkolaras, and S. Le Digabel, “Two decades of blackbox optimization applications,” EURO Journal on Computational Optimization 9, 100011 (2021). 3K. Terayama, M. Sumita, R. Tamura, and K. Tsuda, “Black-box opti- mization for automated discovery,” Accounts of Chemical Research 54, 1334–1346 (2021). 4W....

    work page 2021

  2. [2]

    A Tutorial on Bayesian Optimization

    pp. 81–100. 5V . Belevitch, “Summary of the history of circuit theory,” Proceedings of the IRE 50, 848–855 (1962). 6N. Wiener, Cybernetics or Control and Communication in the Animal and the Machine (The MIT Press, 1961). 7P. I. Frazier, “A tutorial on Bayesian optimization,” (2018), arXiv:1807.02811 [stat.ML]. 8J. Snoek, H. Larochelle, and R. P. Adams, “P...

    work page internal anchor Pith review Pith/arXiv arXiv 1962

  3. [3]

    Bifurcation-based adiabatic quantum computation with a non- linear oscillator network,

    pp. 432–438. 34H. Goto, “Bifurcation-based adiabatic quantum computation with a non- linear oscillator network,” Scientific Reports6, 21686 (2016). 35H. Goto, K. Tatsumura, and A. R. Dixon, “Combinatorial optimization by simulating adiabatic bifurcations in nonlinear hamiltonian systems,” Sci- ence Advances 5, eaav2372 (2019). 36M. W. Johnson, M. H. S. Am...

    work page 2016

  4. [4]

    A Quantum Approximate Optimization Algorithm

    pp. 101–112. 38T. Inagaki, Y . Haribara, K. Igarashi, T. Sonobe, S. Tamate, T. Honjo, A. Marandi, P. L. McMahon, T. Umeki, K. Enbutsu, O. Tadanaga, H. Take- nouchi, K. Aihara, K. Kawarabayashi, K. Inoue, S. Utsunomiya, and H. Takesue, “A coherent Ising machine for 2000-node optimization prob- lems,” Science 354, 603–606 (2016). 39T. Honjo, T. Sonobe, K. I...

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  5. [5]

    and Daulton, Samuel and Letham, Benjamin and Wilson, Andrew Gordon and Bakshy, Eytan , year =

    pp. 131–141. 57T. Akiba, S. Sano, T. Yanase, T. Ohta, and M. Koyama, “Optuna: A next-generation hyperparameter optimization framework,” inProceedings of the 25th ACM SIGKDD International Conference on Knowledge Dis- covery and Data Mining (2019). 58“Gpyopt,”https://sheffieldml.github.io/GPyOpt/. 59K. C. Felton, J. G. Rittig, and A. A. Lapkin, “Summit: Ben...

    work page arXiv 2019

  6. [6]

    GitHub, fmqa,

    pp. 8024–8035. 66“GitHub, fmqa,”https://github.com/tsudalab/fmqa. 67Y . Seki, R. Tamura, and S. Tanaka, “Black-box optimization for integer- variable problems using Ising machines and factorization machines,” (2022), arXiv:2209.01016 [cs.LG]. 68E. Agrell, J. Lassing, E. Strom, and T. Ottosson, “On the optimality of the binary reflected gray code,” IEEE Tr...

    work page arXiv 2022

  7. [7]

    Machine learning framework for quantum sampling of highly constrained, continuous optimization problems,

    p. FTh2M.2. 122B. A. Wilson, Z. A. Kudyshev, A. V . Kildishev, S. Kais, V . M. Shalaev, and A. Boltasseva, “Machine learning framework for quantum sampling of highly constrained, continuous optimization problems,” Applied Physics Reviews 8, 041418 (2021). 123Z. Mao, Y . Matsuda, R. Tamura, and K. Tsuda, “Chemical design with GPU-based Ising machines,” Dig...

    work page 2021

  8. [8]

    Junction tree variational autoen- coder for molecular graph generation,

    introduction to methodology and encoding rules,” Journal of Chemical Information and Computer Sciences 28, 31–36 (1988). 125W. Jin, R. Barzilay, and T. Jaakkola, “Junction tree variational autoen- coder for molecular graph generation,” inProceedings of the 35th Interna- tional Conference on Machine Learning , Proceedings of Machine Learn- ing Research, V ...

    work page 1988

  9. [9]

    Categorical Reparameterization with Gumbel-Softmax

    pp. 2323–2332. 126E. Jang, S. Gu, and B. Poole, “Categorical reparameterization with Gumbel-softmax,” (2017), arXiv:1611.01144 [stat.ML]. 127R. Baynazarov and I. Piontkovskaya, “Binary autoencoder for text model- ing,” inArtificial Intelligence and Natural Language, edited by D. Ustalov, A. Filchenkov, and L. Pivovarova (Springer International Publishing, Cham,

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  10. [10]

    Quantum-classical com- putational molecular design of deuterated high-efficiency OLED emitters,

    pp. 139–150. 128Q. Gao, G. O. Jones, T. Kobayashi, M. Sugawara, H. Yamashita, H. Kawaguchi, S. Tanaka, and N. Yamamoto, “Quantum-classical com- putational molecular design of deuterated high-efficiency OLED emitters,” Intelligent Computing 2, 0037 (2023). 129“IBMQ,”https://www.ibm.com/quantum/technology. 130G. Schneider, “Automating drug discovery,” Natur...

    work page 2023

  11. [11]

    Batch Bayesian optimization via simu- lation matching,

    pp. 648–657. 137J. Azimi, A. Fern, and X. Fern, “Batch Bayesian optimization via simu- lation matching,” in Advances in Neural Information Processing Systems, V ol. 23, edited by J. Lafferty, C. Williams, J. Shawe-Taylor, R. Zemel, and A. Culotta (Curran Associates, Inc., 2010). 138Z. Dai, Q. P. Nguyen, S. Tay, D. Urano, R. Leong, B. K. H. Low, and P. Jai...

    work page 2010

  12. [12]

    Space-efficient binary optimiza- tion for variational quantum computing,

    pp. 36476–36506. 139A. Glos, A. Krawiec, and Z. Zimborás, “Space-efficient binary optimiza- tion for variational quantum computing,” npj Quantum Information 8, 39 (2022). 140K. Domino, A. Kundu, Ö. Salehi, and K. Krawiec, “Quadratic and higher- order unconstrained binary optimization of railway rescheduling for quan- tum computing,” Quantum Information Pr...

    work page 2022