# Function Smoothing Regularization for Precision Factorization Machine Annealing in Continuous Variable Optimization Problems

arXiv: https://arxiv.org/abs/2407.04393 · HTML: https://mlsanity.com/paper/2407.04393/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 4 of 4)

- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [Implementation of Trained Factorization Machine Recommendation System on Quantum Annealer](https://mlsanity.com/paper/2210.12953/) (2022)

## Built on by (most cited first, 2 of 2)

- [Extended Factorization Machine Annealing for Rapid Discovery of Transparent Conducting Materials](https://mlsanity.com/paper/2507.23160/) (2025)
- [Stage-dependent integer-binary encoding in factorization-machine black-box optimization](https://mlsanity.com/paper/2606.23188/) (2026)

## Abstract (arXiv)

Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of the Hamiltonian function surface obtained by factorization machine (FM) have been overlooked. This study shows that in the widely common case where real numbers are represented by a combination of binary variables, the function surface of the Hamiltonian obtained by FM can be very noisy. This noise interferes with the inherent capabilities of quantum annealing and is likely to be a substantial cause of problems previously considered unsolvable due to the limitations of FMQA performance. The origin of the noise is identified and a simple, general method is proposed to prevent its occurrence. The generalization performance of the proposed method and its ability to solve practical problems is demonstrated.