# Unconstrained Stochastic CCA: Unifying Multiview and Self-Supervised Learning

arXiv: https://arxiv.org/abs/2310.01012 · HTML: https://mlsanity.com/paper/2310.01012/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2023.

## Built on by (most cited first, 7 of 7)

- [Contrastive Predictive Coding Done Right for Mutual Information Estimation](https://mlsanity.com/paper/2510.25983/) (2025)
- [When to Align, When to Predict: A Phase Diagram for Multimodal Learning](https://mlsanity.com/paper/2606.11190/) (2026)
- [Revisiting Orbital Minimization Method for Neural Operator Decomposition](https://mlsanity.com/paper/2510.21952/) (2025)
- [PEIRA: Learning Predictive Encoders through Inter-View Regressor Alignment](https://mlsanity.com/paper/2605.17671/) (2026)
- [TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees](https://mlsanity.com/paper/2607.27027/) (2026)
- [Increasing Width Allows Greedy Layer-wise Training to Rival End-to-End Backpropagation in Self-Supervised Learning](https://mlsanity.com/paper/2610.00753/) (2026)
- [Revisiting Visual Representation Enhancement of VLMs via Kernel Canonical Correlation Analysis](https://mlsanity.com/paper/2610.02718/) (2026)

## Abstract (arXiv)

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. Our algorithms show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These improvements allow us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 features. Finally, we apply our algorithms to match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to clarify the links between these methods and classical CCA, laying the groundwork for future insights.