# A Generalized EigenGame with Extensions to Multiview Representation Learning

arXiv: https://arxiv.org/abs/2211.11323 · HTML: https://mlsanity.com/paper/2211.11323/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Contrastive and Non-Contrastive Self-Supervised Learning Recover Global and Local Spectral Embedding Methods](https://mlsanity.com/paper/2205.11508/) (2022)
- [A survey of multimodal deep generative models](https://mlsanity.com/paper/2207.02127/) (2022)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [EigenGame: PCA as a Nash Equilibrium](https://mlsanity.com/paper/2010.00554/) (2020)
- [EigenGame Unloaded: When playing games is better than optimizing](https://mlsanity.com/paper/2102.04152/) (2021)
- [Stochastic Approximation for Canonical Correlation Analysis](https://mlsanity.com/paper/1702.06818/) (2017)
- [Stochastic Approximation on Riemannian manifolds](https://mlsanity.com/paper/1711.10754/) (2017)
- [An Online Riemannian PCA for Stochastic Canonical Correlation Analysis](https://mlsanity.com/paper/2106.07479/) (2021)
- [Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations](https://mlsanity.com/paper/1510.02054/) (2015)
- [Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems](https://mlsanity.com/paper/2112.14738/) (2021)

## Abstract (arXiv)

Generalized Eigenvalue Problems (GEPs) encompass a range of interesting dimensionality reduction methods. Development of efficient stochastic approaches to these problems would allow them to scale to larger datasets. Canonical Correlation Analysis (CCA) is one example of a GEP for dimensionality reduction which has found extensive use in problems with two or more views of the data. Deep learning extensions of CCA require large mini-batch sizes, and therefore large memory consumption, in the stochastic setting to achieve good performance and this has limited its application in practice. Inspired by the Generalized Hebbian Algorithm, we develop an approach to solving stochastic GEPs in which all constraints are softly enforced by Lagrange multipliers. Then by considering the integral of this Lagrangian function, its pseudo-utility, and inspired by recent formulations of Principal Components Analysis and GEPs as games with differentiable utilities, we develop a game-theory inspired approach to solving GEPs. We show that our approaches share much of the theoretical grounding of the previous Hebbian and game theoretic approaches for the linear case but our method permits extension to general function approximators like neural networks for certain GEPs for dimensionality reduction including CCA which means our method can be used for deep multiview representation learning. We demonstrate the effectiveness of our method for solving GEPs in the stochastic setting using canonical multiview datasets and demonstrate state-of-the-art performance for optimizing Deep CCA.