# On computable learning of continuous features

arXiv: https://arxiv.org/abs/2111.14630 · HTML: https://mlsanity.com/paper/2111.14630/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 24 Nov 2021.

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

- [PAC Learning, VC Dimension, and the Arithmetic Hierarchy](https://mlsanity.com/paper/1406.1111/) (2014)
- [Weihrauch Complexity in Computable Analysis](https://mlsanity.com/paper/1707.03202/) (2017)
- [A Computability Perspective on (Verified) Machine Learning](https://mlsanity.com/paper/2102.06585/) (2021)
- [Learning Theory in the Arithmetic Hierarchy](https://mlsanity.com/paper/1302.7069/) (2013)

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

- [On characterizations of learnability with computable learners](https://mlsanity.com/paper/2202.05041/) (2022)
- [Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning](https://mlsanity.com/paper/2511.02644/) (2025)

## Abstract (arXiv)

We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong Weihrauch degree of an ERM learner under more general conditions. We also give a presentation of a hypothesis class that does not admit any proper computable PAC learner with computable sample function, despite the underlying class being PAC learnable.