mlsanityData to 7 Oct 2026

The Galerkin method beats Graph-Based Approaches for Spectral Algorithms

arXiv 2306.00742 ↗First posted 1 Jun 2023cs.LG cs.AI stat.MLcited by 6

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Abstract (arXiv)

Historically, the machine learning community has derived spectral decompositions from graph-based approaches. We break with this approach and prove the statistical and computational superiority of the Galerkin method, which consists in restricting the study to a small set of test functions. In particular, we introduce implementation tricks to deal with differential operators in large dimensions with structured kernels. Finally, we extend on the core principles beyond our approach to apply them to non-linear spaces of functions, such as the ones parameterized by deep neural networks, through loss-based optimization procedures.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 25 of its 68 references that are in the map. First posted on arXiv 1 Jun 2023.

Builds on

25 of 68 references.

References · 25

  1. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 11,979
  2. 2021Barlow Twins: Self-Supervised Learning via Redundancy Reductioncited by 1,818
  3. 2021VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learningcited by 1,013
  4. 2014Convex Optimization: Algorithms and Complexitycited by 569
  5. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  6. 2015An Introduction to Matrix Concentration Inequalitiescited by 391
  7. 2021Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Losscited by 311
  8. 2020Whitening for Self-Supervised Representation Learningcited by 278
  9. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 230
  10. 2016Generalization Properties of Learning with Random Featurescited by 163
  11. 2020Predicting What You Already Know Helps: Provable Self-Supervised Learningcited by 152
  12. 2022Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methodscited by 146
13 more
  1. 2015Less is More: Nystr"om Computational Regularizationcited by 89
  2. 2020Kernel methods through the roof: handling billions of points efficientlycited by 88
  3. 2023The SSL Interplay: Augmentations, Inductive Bias, and Generalizationcited by 40
  4. 2019Machine learning in acoustics: theory and applicationscited by 36
  5. 2020Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approachcited by 35
  6. 2022Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functionscited by 32
  7. 2022Contrastive Laplacian Eigenmapscited by 24
  8. 2022Neural Eigenfunctions Are Structured Representation Learnerscited by 16
  9. 2020Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learningcited by 14
  10. 2021Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networkscited by 13
  11. 2022On minimal variations for unsupervised representation learningcited by 6
  12. 2023Kernelized Diffusion mapscited by 5
  13. 2023How many samples are needed to leverage smoothness?cited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 0; 2026: 3.

6 papers.

  1. 2024Learning the Infinitesimal Generator of Stochastic Diffusion Processescited by 9
  2. 2024Laplace Transform Based Low-Complexity Learning of Continuous Markov Semigroupscited by 7
  3. 2024From Biased to Unbiased Dynamics: An Infinitesimal Generator Approachcited by 6
  4. 2026A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Controlcited by 0
  5. 2026Adaptive Kernel Selection for Kernelized Diffusion Mapscited by 0
  6. 2026Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedbackcited by 0