# Elucidating linear programs by neural encodings

## TL;DR

This paper explores how to make linear programs more explainable by encoding them as neural networks, enabling the use of attribution methods for better understanding.

## Contribution

The novelty lies in adapting attribution methods for linear programs by representing them as neural networks.

## Key findings

- Neural encodings of LPs enable the use of explanation methods like Saliency and LIME.
- The approach works even for large-scale LPs with 10,000 dimensions.
- At low perturbation levels, Saliency and LIME produce indistinguishable results.

## Abstract

Linear Programs (LPs) are one of the major building blocks of AI and have championed recent strides in differentiable optimizers for learning systems. While efficient solvers exist for even high-dimensional LPs, explaining their solutions has not received much attention yet, as explainable artificial intelligence (XAI) has mostly focused on deep learning models. LPs are mostly considered white-box and thus assumed simple to explain, but we argue that they are not easy to understand in terms of relationships between inputs and outputs. To mitigate this rather non-explainability of LPs we show how to adapt attribution methods by encoding LPs in a neural fashion. The encoding functions consider aspects such as the feasibility of the decision space, the cost attached to each input, and the distance to special points of interest. Using a variety of LPs, including a very large-scale LP with 10k dimensions, we demonstrate the usefulness of explanation methods using our neural LP encodings, although the attribution methods Saliency and LIME are indistinguishable for low perturbation levels. In essence, we demonstrate that LPs can and should be explained, which can be achieved by representing an LP as a neural network.