# A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity

arXiv: https://arxiv.org/abs/2509.20618 · HTML: https://mlsanity.com/paper/2509.20618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [A Characterization of Multiclass Learnability](https://mlsanity.com/paper/2203.01550/) (2022)
- [Optimal Learners for Multiclass Problems](https://mlsanity.com/paper/1405.2420/) (2014)
- [Universal Rates for Multiclass Learning](https://mlsanity.com/paper/2307.02066/) (2023)
- [Refined Risk Bounds for Unbounded Losses via Transductive Priors](https://mlsanity.com/paper/2410.21621/) (2024)

## Abstract (arXiv)

We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of citeanthony2000function,alon1997scale. Moreover, we show that the gapped dimensions lead to lower bounds on offset Rademacher averages, thereby strengthening existing approaches for proving lower bounds on rates of convergence in statistical and online learning.