# Generalisation and benign over-fitting for linear regression onto random functional covariates

arXiv: https://arxiv.org/abs/2508.13895 · HTML: https://mlsanity.com/paper/2508.13895/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Benign overfitting in ridge regression](https://mlsanity.com/paper/2009.14286/) (2020)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Generalization in Kernel Regression Under Realistic Assumptions](https://mlsanity.com/paper/2312.15995/) (2023)
- [An elementary analysis of ridge regression with random design](https://mlsanity.com/paper/2203.08564/) (2022)
- [Risk and cross validation in ridge regression with correlated samples](https://mlsanity.com/paper/2408.04607/) (2024)
- [A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression](https://mlsanity.com/paper/2310.00987/) (2023)
- [Asymptotics of Linear Regression with Linearly Dependent Data](https://mlsanity.com/paper/2412.03702/) (2024)
- [Benign Overfitting in Time Series Linear Models with Over-Parameterization](https://mlsanity.com/paper/2204.08369/) (2022)
- [ROTI-GCV: Generalized Cross-Validation for right-ROTationally Invariant Data](https://mlsanity.com/paper/2406.11666/) (2024)

## Built on by (most cited first, 1 of 1)

- [Deep Exploration of Epoch-wise Double Descent in Noisy Data: Signal Separation, Large Activation, and Benign Overfitting](https://mlsanity.com/paper/2601.08316/) (2026)

## Abstract (arXiv)

We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating p random, means-square continuous functions over a latent metric space at n random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the n covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, 4-th order moment, and other regularity conditions, we obtain probabilistic bounds on a notion of predictive excess risk adapted to our random functional covariate setting, making use of recent results of Barzilai and Shamir. We derive convergence rates in regimes where p grows suitably fast relative to n, illustrating interplay between ingredients of the model in determining convergence behaviour and the role of additive covariate noise in benign-overfitting.