# Approximate Description Length, Covering Numbers, and VC Dimension

arXiv: https://arxiv.org/abs/2209.12882 · HTML: https://mlsanity.com/paper/2209.12882/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 26 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [Generalization Bounds for Neural Networks via Approximate Description Length](https://mlsanity.com/paper/1910.05697/) (2019)

## Abstract (arXiv)

Recently, Daniely and Granot [arXiv:1910.05697] introduced a new notion of complexity called Approximate Description Length (ADL). They used it to derive novel generalization bounds for neural networks, that despite substantial work, were out of reach for more classical techniques such as discretization, Covering Numbers and Rademacher Complexity. In this paper we explore how ADL relates to classical notions of function complexity such as Covering Numbers and VC Dimension. We find that for functions whose range is the reals, ADL is essentially equivalent to these classical complexity measures. However, this equivalence breaks for functions with high dimensional range.