# Predictive Self-Supervised Learning Provably Identifies Stochastic Signals under Nuisance

arXiv: https://arxiv.org/abs/2609.37789 · HTML: https://mlsanity.com/paper/2609.37789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 31 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Introduction to Latent Variable Energy-Based Models: A Path Towards Autonomous Machine Intelligence](https://mlsanity.com/paper/2306.02572/) (2023)
- [Latent Action Learning Requires Supervision in the Presence of Distractors](https://mlsanity.com/paper/2502.00379/) (2025)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Reverse Engineering Self-Supervised Learning](https://mlsanity.com/paper/2305.15614/) (2023)
- [Representation Uncertainty in Self-Supervised Learning as Variational Inference](https://mlsanity.com/paper/2203.11437/) (2022)
- [The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning](https://mlsanity.com/paper/2307.10907/) (2023)
- [InfoNCE is variational inference in a recognition parameterised model](https://mlsanity.com/paper/2107.02495/) (2021)
- [Self-supervised contrastive learning performs non-linear system identification](https://mlsanity.com/paper/2410.14673/) (2024)
- [A Probabilistic Model Behind Self-Supervised Learning](https://mlsanity.com/paper/2402.01399/) (2024)
- [Understanding Self-Supervised Learning via Latent Distribution Matching](https://mlsanity.com/paper/2605.03517/) (2026)

## Abstract (arXiv)

Self-supervised learning (SSL) by predicting in latent space, without generating the input data itself, learns highly abstract, useful representations. Intuitively, this success is often attributed to its ability to discard nuisance information that is irrelevant to prediction. However, this poses a conundrum: both stochastic variation in a prediction-relevant latent signal and true nuisance make observations partly unpredictable; how could they be distinguished? Surprisingly, we prove that common SSL methods can achieve exactly this, by implicitly instantiating a latent-variable model with stochastic dynamics and observation-private nuisance. We trace their ability to recover the stochastic signal to two complementary principles: Predictive mutual information maximization ensures that representations retain the information needed for prediction, while latent distribution matching constrains how this information is encoded, thereby making the retained signal identifiable. We confirm this identifiability result in simulations for Gaussian predictors, which recover the true signal up to an affine transformation even in dynamic, nuisance-laden environments.