# Machines Explaining Linear Programs

arXiv: https://arxiv.org/abs/2206.07194 · HTML: https://mlsanity.com/paper/2206.07194/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 17 of 17)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)
- [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020)
- [Neural Network Attributions: A Causal Perspective](https://mlsanity.com/paper/1902.02302/) (2019)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Understanding Integrated Gradients with SmoothTaylor for Deep Neural Network Attribution](https://mlsanity.com/paper/2004.10484/) (2020)

## Abstract (arXiv)

There has been a recent push in making machine learning models more interpretable so that their performance can be trusted. Although successful, these methods have mostly focused on the deep learning methods while the fundamental optimization methods in machine learning such as linear programs (LP) have been left out. Even if LPs can be considered as whitebox or clearbox models, they are not easy to understand in terms of relationships between inputs and outputs. As a linear program only provides the optimal solution to an optimization problem, further explanations are often helpful. In this work, we extend the attribution methods for explaining neural networks to linear programs. These methods explain the model by providing relevance scores for the model inputs, to show the influence of each input on the output. Alongside using classical gradient-based attribution methods we also propose a way to adapt perturbation-based attribution methods to LPs. Our evaluations of several different linear and integer problems showed that attribution methods can generate useful explanations for linear programs. However, we also demonstrate that using a neural attribution method directly might come with some drawbacks, as the properties of these methods on neural networks do not necessarily transfer to linear programs. The methods can also struggle if a linear program has more than one optimal solution, as a solver just returns one possible solution. Our results can hopefully be used as a good starting point for further research in this direction.