# Matrix factorization with neural networks

arXiv: https://arxiv.org/abs/2212.02105 · HTML: https://mlsanity.com/paper/2212.02105/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 35 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 2 of 2)

- [Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks](https://mlsanity.com/paper/2201.00032/) (2021)
- [Bayesian reconstruction of memories stored in neural networks from their connectivity](https://mlsanity.com/paper/2105.07416/) (2021)

## Built on by (most cited first, 6 of 6)

- [Bayes-optimal learning of an extensive-width neural network from quadratically many samples](https://mlsanity.com/paper/2408.03733/) (2024)
- [On the phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariance](https://mlsanity.com/paper/2411.01974/) (2024)
- [Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokens](https://mlsanity.com/paper/2410.18858/) (2024)
- [The Decimation Scheme for Symmetric Matrix Factorization](https://mlsanity.com/paper/2307.16564/) (2023)
- [Gradient flow on extensive-rank positive semi-definite matrix denoising](https://mlsanity.com/paper/2303.09474/) (2023)
- [Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning](https://mlsanity.com/paper/2307.15778/) (2023)

## Abstract (arXiv)

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. We introduce a decimation algorithm based on ground-state search of the neural network, which shows performances that match the theoretical prediction.