# Factorization Machine with Quadratic-Optimization Annealing for RNA Inverse Folding and Evaluation of Binary-Integer Encoding and Nucleotide Assignment

arXiv: https://arxiv.org/abs/2602.16643 · HTML: https://mlsanity.com/paper/2602.16643/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 67 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [Learning to Design RNA](https://mlsanity.com/paper/1812.11951/) (2018)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Designing RNA Secondary Structures is Hard](https://mlsanity.com/paper/1710.11513/) (2017)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [SentRNA: Improving computational RNA design by incorporating a prior of human design strategies](https://mlsanity.com/paper/1803.03146/) (2018)
- [Efficient Bit Labeling in Factorization Machines with Annealing for Traveling Salesman Problem](https://mlsanity.com/paper/2407.02091/) (2024)
- [High-Order Epistasis Detection Using Factorization Machine with Quadratic Optimization Annealing and MDR-Based Evaluation](https://mlsanity.com/paper/2601.01860/) (2026)

## 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)

The RNA inverse folding problem aims to identify nucleotide sequences that preferentially adopt a given target secondary structure. While various heuristic and machine learning-based approaches have been proposed, many require a large number of sequence evaluations, which limits their applicability when experimental validation is costly. We propose a method to solve the problem using a factorization machine with quadratic-optimization annealing (FMQA). FMQA is a discrete black-box optimization method reported to obtain high-quality solutions with a limited number of evaluations. Applying FMQA to the problem requires converting nucleotides into binary variables. However, the influence of integer-to-nucleotide assignments and binary-integer encoding on the performance of FMQA has not been thoroughly investigated, even though such choices determine the structure of the surrogate model and the search landscape, and thus can directly affect solution quality. Therefore, this study aims both to establish a novel FMQA framework for RNA inverse folding and to analyze the effects of these assignments and encoding methods. We evaluated all 24 possible assignments of the four nucleotides to the ordered integers (0-3), in combination with four binary-integer encoding methods. Our results demonstrated that one-hot and domain-wall encodings outperform binary and unary encodings in terms of the normalized ensemble defect value. In domain-wall encoding, nucleotides assigned to the boundary integers (0 and 3) appeared with higher frequency. In the RNA inverse folding problem, assigning guanine and cytosine to these boundary integers promoted their enrichment in stem regions, which led to more thermodynamically stable secondary structures than those obtained with one-hot encoding.