mlsanityData to 14 Oct 2026

Matrix factorization with neural networks

arXiv 2212.02105 ↗First posted 5 Dec 2022cond-mat.dis-nn cs.LGcited by 6

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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.

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

2 of 35 references.

References · 2

  1. 2021Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networkscited by 9
  2. 2021Bayesian reconstruction of memories stored in neural networks from their connectivitycited by 2

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Cited by year

Citing papers per year: 2023: 3; 2024: 3.

6 papers.

  1. 2024Bayes-optimal learning of an extensive-width neural network from quadratically many samplescited by 23
  2. 2024On the phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariancecited by 4
  3. 2024Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokenscited by 3
  4. 2023The Decimation Scheme for Symmetric Matrix Factorizationcited by 2
  5. 2023Gradient flow on extensive-rank positive semi-definite matrix denoisingcited by 1
  6. 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1