# On the Rashomon ratio of infinite hypothesis sets

arXiv: https://arxiv.org/abs/2404.17746 · HTML: https://mlsanity.com/paper/2404.17746/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 27 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [Random-projection ensemble classification](https://mlsanity.com/paper/1504.04595/) (2015)
- [Approximation and generalization properties of the random projection classification method](https://mlsanity.com/paper/2108.06339/) (2021)

## Built on by (most cited first, 2 of 2)

- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [The Impact of Stochasticity on the Rashomon Effect in Machine Learning](https://mlsanity.com/paper/2609.32934/) (2026)

## Abstract (arXiv)

Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.