# Learning first-order definable concepts over structures of small degree

## TL;DR

This paper introduces a logical framework for machine learning where concepts are defined by first-order formulas over structures with small degree, demonstrating efficient learnability in polylogarithmic time.

## Contribution

It shows that first-order definable concepts over structures of small degree can be learned efficiently in the PAC setting, combining logic and complexity theory.

## Key findings

- Concepts definable by first-order formulas are learnable in polylogarithmic time.
- The framework applies to structures with polylogarithmic degree.
- Efficient learning is achieved within the PAC model.

## Abstract

We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a background structure of at most polylogarithmic degree can be learned in polylogarithmic time in the "probably approximately correct" learning sense.