mlsanityData to 14 Oct 2026

Dense associative memory for Gaussian distributions

arXiv 2509.23162 ↗First posted 27 Sep 2025cs.LG cs.AI math.STcited by 2

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Abstract (arXiv)

Dense associative memories (DAMs) store and retrieve patterns via energy-function based fixed points, but existing models are limited to vector representations. We extend DAMs to Gaussian densities equipped with the 2-Wasserstein distance. Our framework defines a log-sum-exp energy over stored distributions and a retrieval dynamics aggregating optimal transport maps in a Gibbs-weighted manner. Stationary points correspond to self-consistent Wasserstein barycenters, generalizing classical DAM fixed points. We prove exponential storage capacity and provide quantitative retrieval guarantees under Wasserstein perturbations. We validate the method on synthetic and real-world image (CelebA and CIFAR-10 datasets) and text (text8 and NLI corpus) datasets. By generalizing from vectors to distributions, our work bridges classical DAMs with modern generative modeling and paves way for distributional storage and retrieval in memory-augmented learning.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 29 of its 44 references that are in the map. First posted on arXiv 27 Sep 2025.

Builds on

29 of 44 references.

References · 29

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2017A Broad-Coverage Challenge Corpus for Sentence Understanding through Inferencecited by 2,682
  5. 2021SimCSE: Simple Contrastive Learning of Sentence Embeddingscited by 2,173
  6. 2015Variational Inference with Normalizing Flowscited by 2,170
  7. 2015A large annotated corpus for learning natural language inferencecited by 1,847
  8. 2018Computational Optimal Transportcited by 780
  9. 2020Hopfield Networks is All You Needcited by 475
  10. 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 335
  11. 2016Dense Associative Memory for Pattern Recognitioncited by 236
  12. 2013Fast Computation of Wasserstein Barycenterscited by 216
17 more
  1. 2021The Bayesian Learning Rulecited by 99
  2. 2014Word Representations via Gaussian Embeddingcited by 96
  3. 2022Variational inference via Wasserstein gradient flowscited by 85
  4. 2023Energy Transformercited by 71
  5. 2017Dense Associative Memory is Robust to Adversarial Inputscited by 45
  6. 2023On Sparse Modern Hopfield Modelcited by 42
  7. 2024Uniform Memory Retrieval with Larger Capacity for Modern Hopfield Modelscited by 38
  8. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  9. 2021Hierarchical Associative Memorycited by 34
  10. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 28
  11. 2025Modern Methods in Associative Memorycited by 15
  12. 2025Rectified Point Flow: Generic Point Cloud Pose Estimationcited by 14
  13. 2024Sparse and Structured Hopfield Networkscited by 13
  14. 2025Flowing Datasets with Wasserstein over Wasserstein Gradient Flowscited by 11
  15. 2025Dense Associative Memory with Epanechnikov Energycited by 11
  16. 2024Dense Associative Memory Through the Lens of Random Featurescited by 8
  17. 2023Sentence Representations via Gaussian Embeddingcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamicscited by 0
  2. 2026Graph Memory: Spectral Associative Memory via Dirichlet Energycited by 0