# Infinite Width Limits of Self Supervised Neural Networks

arXiv: https://arxiv.org/abs/2411.11176 · HTML: https://mlsanity.com/paper/2411.11176/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 17 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [On the linearity of large non-linear models: when and why the tangent kernel is constant](https://mlsanity.com/paper/2010.01092/) (2020)
- [The SSL Interplay: Augmentations, Inductive Bias, and Generalization](https://mlsanity.com/paper/2302.02774/) (2023)
- [On the Stepwise Nature of Self-Supervised Learning](https://mlsanity.com/paper/2303.15438/) (2023)
- [Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functions](https://mlsanity.com/paper/2210.01883/) (2022)
- [The Eigenlearning Framework: A Conservation Law Perspective on Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2110.03922/) (2021)
- [What shapes the loss landscape of self-supervised learning?](https://mlsanity.com/paper/2210.00638/) (2022)
- [Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernels](https://mlsanity.com/paper/2302.01629/) (2023)
- [Joint Embedding Self-Supervised Learning in the Kernel Regime](https://mlsanity.com/paper/2209.14884/) (2022)
- [Non-Parametric Representation Learning with Kernels](https://mlsanity.com/paper/2309.02028/) (2023)
- [When can we Approximate Wide Contrastive Models with Neural Tangent Kernels and Principal Component Analysis?](https://mlsanity.com/paper/2403.08673/) (2024)

## Built on by (most cited first, 4 of 4)

- [Interpretable Self-Supervised Learning via Representer Landmarks and Nystr"om Approximation](https://mlsanity.com/paper/2509.24467/) (2025)
- [Theoretical Foundations of Representation Learning using Unlabeled Data: Statistics and Optimization](https://mlsanity.com/paper/2509.18997/) (2025)
- [Revisiting the Neural Tangent Kernel: the role of large width and depth](https://mlsanity.com/paper/2511.07272/) (2025)
- [An Analysis of Self-supervised Pre-training with Dependent Samples](https://mlsanity.com/paper/2609.05031/) (2026)

## Abstract (arXiv)

The NTK is a widely used tool in the theoretical analysis of deep learning, allowing us to look at supervised deep neural networks through the lenses of kernel regression. Recently, several works have investigated kernel models for self-supervised learning, hypothesizing that these also shed light on the behavior of wide neural networks by virtue of the NTK. However, it remains an open question to what extent this connection is mathematically sound -- it is a commonly encountered misbelief that the kernel behavior of wide neural networks emerges irrespective of the loss function it is trained on. In this paper, we bridge the gap between the NTK and self-supervised learning, focusing on two-layer neural networks trained under the Barlow Twins loss. We prove that the NTK of Barlow Twins indeed becomes constant as the width of the network approaches infinity. Our analysis technique is a bit different from previous works on the NTK and may be of independent interest. Overall, our work provides a first justification for the use of classic kernel theory to understand self-supervised learning of wide neural networks. Building on this result, we derive generalization error bounds for kernelized Barlow Twins and connect them to neural networks of finite width.