# Structured Learning Modulo Theories

arXiv: https://arxiv.org/abs/1405.1675 · HTML: https://mlsanity.com/paper/1405.1675/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2014.

## Built on by (most cited first, 5 of 5)

- [Neuro-Symbolic Constraint Programming for Structured Prediction](https://mlsanity.com/paper/2103.17232/) (2021)
- [Learning MAX-SAT from Contextual Examples for Combinatorial Optimisation](https://mlsanity.com/paper/2202.03888/) (2022)
- [SaDe: Learning Models that Provably Satisfy Domain Constraints](https://mlsanity.com/paper/2112.00552/) (2021)
- [Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens](https://mlsanity.com/paper/2205.10157/) (2022)
- [Can Large Language Models put 2 and 2 together? Probing for Entailed Arithmetical Relationships](https://mlsanity.com/paper/2404.19432/) (2024)

## Abstract (arXiv)

Modelling problems containing a mixture of Boolean and numerical variables is a long-standing interest of Artificial Intelligence. However, performing inference and learning in hybrid domains is a particularly daunting task. The ability to model this kind of domains is crucial in "learning to design" tasks, that is, learning applications where the goal is to learn from examples how to perform automatic em de novo design of novel objects. In this paper we present Structured Learning Modulo Theories, a max-margin approach for learning in hybrid domains based on Satisfiability Modulo Theories, which allows to combine Boolean reasoning and optimization over continuous linear arithmetical constraints. The main idea is to leverage a state-of-the-art generalized Satisfiability Modulo Theory solver for implementing the inference and separation oracles of Structured Output SVMs. We validate our method on artificial and real world scenarios.