mlsanityData to 14 Oct 2026

Signal-Plus-Noise Decomposition of Nonlinear Spiked Random Matrix Models

arXiv 2405.18274 ↗First posted 28 May 2024math.ST cs.LG eess.SPcited by 2

Not on the map. Why?

Abstract (arXiv)

In this paper, we study a nonlinear spiked random matrix model where a nonlinear function is applied element-wise to a noise matrix perturbed by a rank-one signal. We establish a signal-plus-noise decomposition for this model and identify precise phase transitions in the structure of the signal components at critical thresholds of signal strength. To demonstrate the applicability of this decomposition, we then utilize it to study new phenomena in the problems of signed signal recovery in nonlinear models and community detection in transformed stochastic block models. Finally, we validate our results through a series of numerical simulations.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 22 of its 55 references that are in the map. First posted on arXiv 28 May 2024.

Builds on

22 of 55 references.

References · 22

  1. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 413
  2. 2017Community Detection and Stochastic Block Modelscited by 319
  3. 2022High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representationcited by 150
  4. 2021Learning curves of generic features maps for realistic datasets with a teacher-student modelcited by 126
  5. 2020The Gaussian equivalence of generative models for learning with shallow neural networkscited by 113
  6. 2020The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalizationcited by 101
  7. 2017A Random Matrix Approach to Neural Networkscited by 80
  8. 2024The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponentscited by 52
  9. 2023A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networkscited by 49
  10. 2024Asymptotics of feature learning in two-layer networks after one gradient-stepcited by 38
  11. 2018Optimality and Sub-optimality of PCA I: Spiked Random Matrix Modelscited by 33
  12. 2022Spectral Evolution and Invariance in Linear-width Neural Networkscited by 30
10 more
  1. 2020What causes the test error? Going beyond bias-variance via ANOVAcited by 28
  2. 2024Nonlinear spiked covariance matrices and signal propagation in deep neural networkscited by 26
  3. 2015MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channelcited by 22
  4. 2019A Random Matrix Perspective on Mixtures of Nonlinearities for Deep Learningcited by 20
  5. 2018Fundamental limits of detection in the spiked Wigner modelcited by 18
  6. 2023Demystifying Disagreement-on-the-Line in High Dimensionscited by 12
  7. 2018Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling methodcited by 11
  8. 2015Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergencecited by 9
  9. 2023Optimal Algorithms for the Inhomogeneous Spiked Wigner Modelcited by 8
  10. 2023Detection problems in the spiked matrix modelscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspectivecited by 8
  2. 2026Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descentcited by 0