# A Random Matrix Theory of Masked Self-Supervised Regression

arXiv: https://arxiv.org/abs/2601.23208 · HTML: https://mlsanity.com/paper/2601.23208/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 56 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [Generalisation error in learning with random features and the hidden manifold model](https://mlsanity.com/paper/2002.09339/) (2020)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [A Random Matrix Approach to Neural Networks](https://mlsanity.com/paper/1702.05419/) (2017)
- [Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks](https://mlsanity.com/paper/2005.11879/) (2020)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [Scaling and renormalization in high-dimensional regression](https://mlsanity.com/paper/2405.00592/) (2024)
- [A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks](https://mlsanity.com/paper/2310.07891/) (2023)
- [High-dimensional analysis of double descent for linear regression with random projections](https://mlsanity.com/paper/2303.01372/) (2023)
- [Deterministic equivalent and error universality of deep random features learning](https://mlsanity.com/paper/2302.00401/) (2023)
- [On the Spectrum of Random Features Maps of High Dimensional Data](https://mlsanity.com/paper/1805.11916/) (2018)
- [A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator](https://mlsanity.com/paper/2403.08938/) (2024)
- [Eigenvalue distribution of nonlinear models of random matrices](https://mlsanity.com/paper/1904.03090/) (2019)
- [An Equivalence Principle for the Spectrum of Random Inner-Product Kernel Matrices with Polynomial Scalings](https://mlsanity.com/paper/2205.06308/) (2022)
- [Asymptotics of Random Feature Regression Beyond the Linear Scaling Regime](https://mlsanity.com/paper/2403.08160/) (2024)
- [A distributional simplicity bias in the learning dynamics of transformers](https://mlsanity.com/paper/2410.19637/) (2024)
- [Dimension-free deterministic equivalents and scaling laws for random feature regression](https://mlsanity.com/paper/2405.15699/) (2024)
- [Precise Learning Curves and Higher-Order Scaling Limits for Dot Product Kernel Regression](https://mlsanity.com/paper/2205.14846/) (2022)
- [Mapping of attention mechanisms to a generalized Potts model](https://mlsanity.com/paper/2304.07235/) (2023)
- [A Random Matrix Theory Perspective on the Spectrum of Learned Features and Asymptotic Generalization Capabilities](https://mlsanity.com/paper/2410.18938/) (2024)
- [Asymptotics of Learning with Deep Structured (Random) Features](https://mlsanity.com/paper/2402.13999/) (2024)

## Abstract (arXiv)

In the era of transformer models, masked self-supervised learning (SSL) has become a foundational training paradigm. A defining feature of masked SSL is that training aggregates predictions across many masking patterns, giving rise to a joint, matrix-valued predictor rather than a single vector-valued estimator. This object encodes how coordinates condition on one another and poses new analytical challenges. We develop a precise high-dimensional analysis of masked modeling objectives in the proportional regime where the number of samples scales with the ambient dimension. Our results provide explicit expressions for the generalization error and characterize the spectral structure of the learned predictor, revealing how masked modeling extracts structure from data. For spiked covariance models, we show that the joint predictor undergoes a Baik--Ben Arous--P'ech'e (BBP)-type phase transition, identifying when masked SSL begins to recover latent signals. Finally, we identify structured regimes in which masked self-supervised learning provably outperforms PCA, highlighting potential advantages of SSL objectives over classical unsupervised methods