# The Integer Linear Programming Inference Cookbook

arXiv: https://arxiv.org/abs/2307.00171 · HTML: https://mlsanity.com/paper/2307.00171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 75 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Logic-Guided Data Augmentation and Regularization for Consistent Question Answering](https://mlsanity.com/paper/2004.10157/) (2020)
- [A Logic-Driven Framework for Consistency of Neural Models](https://mlsanity.com/paper/1909.00126/) (2019)
- [Joint Reasoning for Temporal and Causal Relations](https://mlsanity.com/paper/1906.04941/) (2019)
- [Joint Constrained Learning for Event-Event Relation Extraction](https://mlsanity.com/paper/2010.06727/) (2020)
- [Augmenting Neural Networks with First-order Logic](https://mlsanity.com/paper/1906.06298/) (2019)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Improving Temporal Relation Extraction with a Globally Acquired Statistical Resource](https://mlsanity.com/paper/1804.06020/) (2018)
- [Modeling Content and Context with Deep Relational Learning](https://mlsanity.com/paper/2010.10453/) (2020)
- [Structured Tuning for Semantic Role Labeling](https://mlsanity.com/paper/2005.00496/) (2020)
- [A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing](https://mlsanity.com/paper/1405.5208/) (2014)
- [Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Study](https://mlsanity.com/paper/2107.13646/) (2021)
- [Learning to Speed Up Structured Output Prediction](https://mlsanity.com/paper/1806.04245/) (2018)
- [RockIt: Exploiting Parallelism and Symmetry for MAP Inference in Statistical Relational Models](https://mlsanity.com/paper/1304.4379/) (2013)

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

- [Mapping the Course for Prompt-based Structured Prediction](https://mlsanity.com/paper/2508.15090/) (2025)
- [Improving Language Identification for Code-Switched Utterances with Integer Linear Programming](https://mlsanity.com/paper/2609.05099/) (2026)

## Abstract (arXiv)

Over the years, integer linear programs have been employed to model inference in many natural language processing problems. This survey is meant to guide the reader through the process of framing a new inference problem as an instance of an integer linear program and is structured as a collection of recipes. At the end, we will see two worked examples to illustrate the use of these recipes.