mlsanityData to 14 Oct 2026

EigenGame: PCA as a Nash Equilibrium

arXiv 2010.00554 ↗First posted 1 Oct 2020cs.LG stat.MLcited by 39

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Abstract (arXiv)

We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA game and the behavior of its gradient based updates. The resulting algorithm -- which combines elements from Oja's rule with a generalized Gram-Schmidt orthogonalization -- is naturally decentralized and hence parallelizable through message passing. We demonstrate the scalability of the algorithm with experiments on large image datasets and neural network activations. We discuss how this new view of PCA as a differentiable game can lead to further algorithmic developments and insights.

Key facts. Cited by 39 papers in the map (data through 14 Oct 2026). First posted on arXiv 1 Oct 2020.

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Citing papers per year: 2021: 4; 2022: 17; 2023: 6; 2024: 3; 2025: 6; 2026: 3.

39 papers.

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  2. 2022Remember the Past: Distilling Datasets into Addressable Memories for Neural Networkscited by 104
  3. 2023Heterogeneous-Agent Reinforcement Learningcited by 69
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  5. 2022NeuralEF: Deconstructing Kernels by Deep Neural Networkscited by 27
  6. 2022On the Limitations of Elo: Real-World Games, are Transitive, not Additivecited by 23
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  9. 2024Operator SVD with Neural Networks via Nested Low-Rank Approximationcited by 13
  10. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  11. 2022A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithmscited by 8
  12. 2022A Novel Stochastic Gradient Descent Algorithm for Learning Principal Subspacescited by 7
27 more
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  4. 2022Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environmentscited by 2
  5. 2023Representations and Exploration for Deep Reinforcement Learning using Singular Value Decompositioncited by 2
  6. 2023Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithmscited by 2
  7. 2022PixelGame: Infrared small target segmentation as a Nash equilibriumcited by 1
  8. 2023Bridging Neural and Symbolic Representations with Transitional Dictionary Learningcited by 1
  9. 2023On the Error-Propagation of Inexact Hotelling's Deflation for Principal Component Analysiscited by 1
  10. 2024Rethinking Teacher-Student Curriculum Learning through the Cooperative Mechanics of Experiencecited by 1
  11. 2025Generalizable Spectral Embedding with an Application to UMAPcited by 1
  12. 2025Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflationcited by 1
  13. 2021A Non-Negative Matrix Factorization Gamecited by 0
  14. 2021Speeding up PCA with primingcited by 0
  15. 2022Self-consistent Gradient-like Eigen Decomposition in Solving Schr"odinger Equationscited by 0
  16. 2022Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspectivecited by 0
  17. 2022The Symmetric Generalized Eigenvalue Problem as a Nash Equilibriumcited by 0
  18. 2022Stochastic Parallelizable Eigengap Dilation for Large Graph Clusteringcited by 0
  19. 2022Principal Component Classificationcited by 0
  20. 2022A Generalized EigenGame with Extensions to Multiview Representation Learningcited by 0
  21. 2024Nash Equilibria via Stochastic Eigendecompositioncited by 0
  22. 2025Quantum EigenGame for excited state calculationcited by 0
  23. 2025Revisiting Orbital Minimization Method for Neural Operator Decompositioncited by 0
  24. 2025Eigenfunction Extraction for Ordered Representation Learningcited by 0
  25. 2026NeuraLSP: A Neural Spectral Preconditioner for Accelerating PDE Solverscited by 0
  26. 2026AdaPaD: Adaptive Parallel Deflation for PEFT with Self-Correcting Rank Discoverycited by 0
  27. 2026Learning Orthonormal Bases for Function Spacescited by 0