# Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation

arXiv: https://arxiv.org/abs/2605.10290 · HTML: https://mlsanity.com/paper/2605.10290/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 11 May 2026.

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

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [A Survey of Data Augmentation Approaches for NLP](https://mlsanity.com/paper/2105.03075/) (2021)
- [Fast AutoAugment](https://mlsanity.com/paper/1905.00397/) (2019)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [An Empirical Survey of Data Augmentation for Time Series Classification with Neural Networks](https://mlsanity.com/paper/2007.15951/) (2020)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [A Survey on Data Augmentation for Text Classification](https://mlsanity.com/paper/2107.03158/) (2021)
- [Faster AutoAugment: Learning Augmentation Strategies using Backpropagation](https://mlsanity.com/paper/1911.06987/) (2019)
- [Data Augmentation techniques in time series domain: A survey and taxonomy](https://mlsanity.com/paper/2206.13508/) (2022)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learning](https://mlsanity.com/paper/2505.12477/) (2025)
- [Deterministic equivalent and error universality of deep random features learning](https://mlsanity.com/paper/2302.00401/) (2023)
- [The good, the bad and the ugly sides of data augmentation: An implicit spectral regularization perspective](https://mlsanity.com/paper/2210.05021/) (2022)
- [Image Data Augmentation Approaches: A Comprehensive Survey and Future directions](https://mlsanity.com/paper/2301.02830/) (2023)
- [Precise Asymptotic Analysis of Deep Random Feature Models](https://mlsanity.com/paper/2302.06210/) (2023)
- [A Rainbow in Deep Network Black Boxes](https://mlsanity.com/paper/2305.18512/) (2023)
- [Asymptotics of Learning with Deep Structured (Random) Features](https://mlsanity.com/paper/2402.13999/) (2024)
- [Quantitative deterministic equivalent of sample covariance matrices with a general dependence structure](https://mlsanity.com/paper/2211.13044/) (2022)
- [Non-Asymptotic Analysis of Data Augmentation for Precision Matrix Estimation](https://mlsanity.com/paper/2510.02119/) (2025)

## Abstract (arXiv)

This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a tight characterization of the test error, measured in mean squared error, in terms only of the population quantities of the true data, as well as first and second order statistics of the augmentation scheme. Our results are valid under misspecified feature maps, and for any network architecture where only the last readout layer is trained, and the rest of the network is either frozen or randomly initialized. We specify our results in the case of Gaussian data, and show that our asymptotic characterization is tight in this setting.