Improving FMQA via Initial Training Data Design Considering Marginal Bit Coverage in One-Hot Encoding

Taiga Hayashi; Yuya Seki; Kotaro Terada; Yosuke Mukasa; Shuta Kikuchi; Shu Tanaka

cs.LGMay 6, 2026

Improving FMQA via Initial Training Data Design Considering Marginal Bit Coverage in One-Hot Encoding

Authors: Taiga Hayashi, Yuya Seki, Kotaro Terada, Yosuke Mukasa, Shuta Kikuchi, Shu Tanaka

Organizations: 1Graduate School of Science and Technology, Keio University, Yokohama, Kanagawa 223-8522, Japan · 2Keio Sustainable Quantum Artificial Intelligence Center, Keio University, Minato-ku, Tokyo 108-8345, Japan · 3Quanmatic Inc., Shinjuku-ku, Tokyo 162-0042, Japan · Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Kanagawa 223-8522, Japan · 5Human Biology-Microbiome-Quantum Research Center, Keio University, Minato-ku, Tokyo 108-8345, Japan

Abstract

Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol' sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.

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Jun 22, 2026 · cs.LGJ/K move · Enter open · S save

Stage-dependent integer-binary encoding in factorization-machine black-box optimization

Ryo Ogawa, Mayumi Nakano, Yuya Seki, Shu Tanaka

Graduate School of Science and Technology, Keio University, Kanagawa 223-8522, Japan · Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC), Keio University, Tokyo 108-8345, Japan · Department of Applied Physics and Physico-Informatics, Keio University, Kanagawa 223-8522, Japan · Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University, Tokyo 108-8345, Japan · Green Computing System Research Organization, Waseda University, Shinjuku-ku, Tokyo 162-0042, Japan

Black-box optimization (BBO) deals with problems where objective functions lack explicit analytical forms and are expensive to evaluate. Factorization machine with quadratic-optimization annealing (FMQA) constructs a surrogate model using a factorization machine (FM) and optimizes it with an Ising machine. Conventional FMQA applies a single integer-binary encoding throughout the optimization process, although the encoding best suited to surrogate learning may differ from the one best suited to Ising-machine solution search. We propose a stage-dependent FMQA framework and derive conversion formulas between one-hot and domain-wall QUBO matrices that preserve the surrogate objective over feasible integer states up to an additive constant. We evaluate the OhDw variant, which employs one-hot encoding for learning and domain-wall encoding for search, on the Rastrigin function with input dimensions N = 2 and 5 and discretization levels q = 61 and 301. Across all conditions, the dominant factor governing optimization performance is the encoding used in the learning stage, with one-hot encoding consistently yielding lower residual errors than domain-wall or binary encoding. The additional benefit of switching to domain-wall encoding for solution search is condition-dependent. For N = 5 and q = 301, OhDw achieves a lower residual error and solutions closer to the global optimum than one-hot-only FMQA, whereas for N = 5 and q = 61 the latter achieves a lower residual error. These results indicate that one-hot encoding in the learning stage is the primary performance driver and that stage-dependent encoding can provide further improvement under finer discretization.

Black-Box Optimization Quantum Approximate Optimization Algorithm Cosine Annealing Exploratory Factor Analysis Surrogate Models

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Abstract

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