# Generalization Analysis for Classification on Korobov Space

arXiv: https://arxiv.org/abs/2509.22748 · HTML: https://mlsanity.com/paper/2509.22748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with  ℓ1  and  ℓ0  Controls](https://mlsanity.com/paper/1607.07819/) (2016)
- [Provable approximation properties for deep neural networks](https://mlsanity.com/paper/1509.07385/) (2015)
- [Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions](https://mlsanity.com/paper/2107.00896/) (2021)
- [Rates of Approximation by ReLU Shallow Neural Networks](https://mlsanity.com/paper/2307.12461/) (2023)
- [Approximation of Nonlinear Functionals Using Deep ReLU Networks](https://mlsanity.com/paper/2304.04443/) (2023)

## Abstract (arXiv)

In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex η-norm loss function φ(v)=(1 - v)+η, η≥1. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of Lp approximation of functions from Korobov space X2, p([-1,1]d), 1≤ p ≤ ∞, by the shallow ReLU neural network. This result consists of a novel Fourier analysis