# Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems

arXiv: https://arxiv.org/abs/2602.10037 · HTML: https://mlsanity.com/paper/2602.10037/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)
- [Annealing-Assisted Column Generation for Inequality-Constrained Combinatorial Optimization Problems](https://mlsanity.com/paper/2406.01887/) (2024)

## Built on by (most cited first, 3 of 3)

- [Binary Latent Protein Fitness Landscapes for Quantum Annealing Optimization](https://mlsanity.com/paper/2603.17247/) (2026)
- [Q-BIOLAT: Binary Latent Protein Fitness Landscapes for QUBO-Based Optimization](https://mlsanity.com/paper/2603.27526/) (2026)
- [Stage-dependent integer-binary encoding in factorization-machine black-box optimization](https://mlsanity.com/paper/2606.23188/) (2026)

## Abstract (arXiv)

In black-box combinatorial optimization, objective evaluations are often expensive, so high quality solutions must be found under a limited budget. Factorization machine with quantum annealing (FMQA) builds a quadratic surrogate model from evaluated samples and optimizes it on an Ising machine. However, FMQA requires binary decision variables, and for nonbinary structures such as integer permutations, the choice of binary encoding strongly affects search efficiency. If the encoding fails to reflect the original neighborhood structure, small Hamming moves may not correspond to meaningful modifications in the original solution space, and constrained problems can yield many infeasible candidates that waste evaluations. Recent work combines FMQA with a binary autoencoder (bAE) that learns a compact binary latent code from feasible solutions, yet the mechanism behind its performance gains is unclear. Using a small traveling salesman problem as an interpretable testbed, we show that the bAE reconstructs feasible tours accurately and, compared with manually designed encodings at similar compression, better aligns tour distances with latent Hamming distances, yields smoother neighborhoods under small bit flips, and produces fewer local optima. These geometric properties explain why bAE+FMQA improves the approximation ratio faster while maintaining feasibility throughout optimization, and they provide guidance for designing latent representations for black-box optimization.