# Non-Negative Matrix Factorization Using Non-Von Neumann Computers

arXiv: https://arxiv.org/abs/2512.00675 · HTML: https://mlsanity.com/paper/2512.00675/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 56 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [Massively Parallel Probabilistic Computing with Sparse Ising Machines](https://mlsanity.com/paper/2110.02481/) (2021)
- [Nonnegative/binary matrix factorization with a D-Wave quantum annealer](https://mlsanity.com/paper/1704.01605/) (2017)
- [Adiabatic Quantum Linear Regression](https://mlsanity.com/paper/2008.02355/) (2020)
- [Non-negative Matrix Factorization: Robust Extraction of Extended Structures](https://mlsanity.com/paper/1712.10317/) (2017)
- [Semi-supervised Classification of Malware Families Under Extreme Class Imbalance via Hierarchical Non-Negative Matrix Factorization with Automatic Model Selection](https://mlsanity.com/paper/2309.06643/) (2023)
- [Reverse Annealing for Nonnegative/Binary Matrix Factorization](https://mlsanity.com/paper/2007.05565/) (2020)
- [Quadratization in discrete optimization and quantum mechanics](https://mlsanity.com/paper/1901.04405/) (2019)
- [Binary matrix factorization on special purpose hardware](https://mlsanity.com/paper/2010.08693/) (2020)
- [Adiabatic Quantum Feature Selection for Sparse Linear Regression](https://mlsanity.com/paper/2106.02357/) (2021)
- [Non-convex Quadratic Programming Using Coherent Optical Networks](https://mlsanity.com/paper/2209.04415/) (2022)
- [Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization](https://mlsanity.com/paper/2501.02114/) (2025)

## Abstract (arXiv)

Non-negative matrix factorization (NMF) is a matrix decomposition problem with applications in unsupervised learning. The general form of this problem (along with many of its variants) is NP-hard in nature. In our work, we explore how this problem could be solved with an energy-based optimization method suitable for certain machines with non-von Neumann architectures. We used the Dirac-3, a device based on the entropy computing paradigm and made by Quantum Computing Inc., to evaluate our approach. Our formulations consist of (i) a quadratic unconstrained binary optimization model (QUBO, suitable for Ising machines) and a quartic formulation that allows for real-valued and integer variables (suitable for machines like the Dirac-3). Although current devices cannot solve large NMF problems, the results of our preliminary experiments are promising enough to warrant further research. For non-negative real matrices, we observed that a fusion approach of first using Dirac-3 and then feeding its results as the initial factor matrices to Scikit-learn's NMF procedure outperforms Scikit-learn's NMF procedure on its own, with default parameters in terms of the error in the reconstructed matrices. For our experiments on non-negative integer matrices, we compared the Dirac-3 device to Google's CP-SAT solver (inside the Or-Tools package) and found that for serial processing, Dirac-3 outperforms CP-SAT in a majority of the cases. We believe that future work in this area might be able to identify domains and variants of the problem where entropy computing (and other non-von Neumann architectures) could offer a clear advantage.