mlsanityData to 14 Oct 2026

A remark on a paper of Krotov and Hopfield [arXiv:2008.06996]

arXiv 2105.15034 ↗First posted 31 May 2021q-bio.NC cs.AI cs.CVcited by 11

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Abstract (arXiv)

In their recent paper titled "Large Associative Memory Problem in Neurobiology and Machine Learning" [arXiv:2008.06996] the authors gave a biologically plausible microscopic theory from which one can recover many dense associative memory models discussed in the literature. We show that the layers of the recent "MLP-mixer" [arXiv:2105.01601] as well as the essentially equivalent model in [arXiv:2105.02723] are amongst them.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 5 of its 5 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

5 of 5 references.

References · 5

  1. 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,446
  2. 2020Hopfield Networks is All You Needcited by 475
  3. 2016Dense Associative Memory for Pattern Recognitioncited by 236
  4. 2020Large Associative Memory Problem in Neurobiology and Machine Learningcited by 112
  5. 2021Do You Even Need Attention? A Stack of Feed-Forward Layers Does Surprisingly Well on ImageNetcited by 61

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 2; 2024: 2; 2025: 3; 2026: 1.

11 papers.

  1. 2023Energy Transformercited by 71
  2. 2022Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Modelscited by 55
  3. 2021Hierarchical Associative Memorycited by 34
  4. 2022Attention in a family of Boltzmann machines emerging from modern Hopfield networkscited by 7
  5. 2024Hierarchical Associative Memory, Parallelized MLP-Mixer, and Symmetry Breakingcited by 5
  6. 2023iMixer: hierarchical Hopfield network implies an invertible, implicit and iterative MLP-Mixercited by 3
  7. 2024Associative memory and dead neuronscited by 1
  8. 2025Neural Learning Rules from Associative Networks Theorycited by 1
  9. 2025Classifying States of the Hopfield Network with Improved Accuracy, Generalization, and Interpretabilitycited by 0
  10. 2025Binding threshold units with artificial oscillatory neuronscited by 0
  11. 2026Controlled Dynamics Attractor Transformercited by 0