# From Linearity to Non-Linearity: How Masked Autoencoders Capture Spatial Correlations

arXiv: https://arxiv.org/abs/2508.15404 · HTML: https://mlsanity.com/paper/2508.15404/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 57 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 30 of 40)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training](https://mlsanity.com/paper/2203.12602/) (2022)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [data2vec: A General Framework for Self-supervised Learning in Speech, Vision and Language](https://mlsanity.com/paper/2202.03555/) (2022)
- [EVA: Exploring the Limits of Masked Visual Representation Learning at Scale](https://mlsanity.com/paper/2211.07636/) (2022)
- [Masked Feature Prediction for Self-Supervised Visual Pre-Training](https://mlsanity.com/paper/2112.09133/) (2021)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [VideoMAE V2: Scaling Video Masked Autoencoders with Dual Masking](https://mlsanity.com/paper/2303.16727/) (2023)
- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [InternVideo: General Video Foundation Models via Generative and Discriminative Learning](https://mlsanity.com/paper/2212.03191/) (2022)
- [Masked Autoencoders As Spatiotemporal Learners](https://mlsanity.com/paper/2205.09113/) (2022)
- [Unified-IO: A Unified Model for Vision, Language, and Multi-Modal Tasks](https://mlsanity.com/paper/2206.08916/) (2022)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Revealing the Dark Secrets of Masked Image Modeling](https://mlsanity.com/paper/2205.13543/) (2022)
- [SemMAE: Semantic-Guided Masking for Learning Masked Autoencoders](https://mlsanity.com/paper/2206.10207/) (2022)
- [FlowFormer++: Masked Cost Volume Autoencoding for Pretraining Optical Flow Estimation](https://mlsanity.com/paper/2303.01237/) (2023)
- [What Do Self-Supervised Vision Transformers Learn?](https://mlsanity.com/paper/2305.00729/) (2023)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [How Mask Matters: Towards Theoretical Understandings of Masked Autoencoders](https://mlsanity.com/paper/2210.08344/) (2022)
- [Masked Frequency Modeling for Self-Supervised Visual Pre-Training](https://mlsanity.com/paper/2206.07706/) (2022)
- [Learning by Reconstruction Produces Uninformative Features For Perception](https://mlsanity.com/paper/2402.11337/) (2024)
- [Understanding Masked Autoencoders via Hierarchical Latent Variable Models](https://mlsanity.com/paper/2306.04898/) (2023)

## Built on by (most cited first, 2 of 2)

- [Learning Representations from Incomplete EHR Data with Dual-Masked Autoencoding](https://mlsanity.com/paper/2602.15159/) (2026)
- [Diagonal Attenuation: A Finite-Sample Correction for PCA](https://mlsanity.com/paper/2609.05796/) (2026)

## Abstract (arXiv)

Masked Autoencoders (MAEs) have emerged as a powerful pretraining technique for vision foundation models. Despite their effectiveness, they require extensive hyperparameter tuning (masking ratio, patch size, encoder/decoder layers) when applied to novel datasets. While prior theoretical works have analyzed MAEs in terms of their attention patterns and hierarchical latent variable models, the connection between MAE hyperparameters and performance on downstream tasks is relatively unexplored. This work investigates how MAEs learn spatial correlations in the input image. We analytically derive the features learned by a linear MAE and show that masking ratio and patch size can be used to select for features that capture short- and long-range spatial correlations. We extend this analysis to non-linear MAEs to show that MAE representations adapt to spatial correlations in the dataset, beyond second-order statistics. Finally, we discuss some insights on how to select MAE hyper-parameters in practice.