# Attributions Beyond Neural Networks: The Linear Program Case

arXiv: https://arxiv.org/abs/2206.07203 · HTML: https://mlsanity.com/paper/2206.07203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [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)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Fast Axiomatic Attribution for Neural Networks](https://mlsanity.com/paper/2111.07668/) (2021)

## Abstract (arXiv)

Linear Programs (LPs) have been one of the building blocks in machine learning and have championed recent strides in differentiable optimizers for learning systems. While there exist solvers for even high-dimensional LPs, understanding said high-dimensional solutions poses an orthogonal and unresolved problem. We introduce an approach where we consider neural encodings for LPs that justify the application of attribution methods from explainable artificial intelligence (XAI) designed for neural learning systems. The several encoding functions we propose take into account aspects such as feasibility of the decision space, the cost attached to each input, or the distance to special points of interest. We investigate the mathematical consequences of several XAI methods on said neural LP encodings. We empirically show that the attribution methods Saliency and LIME reveal indistinguishable results up to perturbation levels, and we propose the property of Directedness as the main discriminative criterion between Saliency and LIME on one hand, and a perturbation-based Feature Permutation approach on the other hand. Directedness indicates whether an attribution method gives feature attributions with respect to an increase of that feature. We further notice the baseline selection problem beyond the classical computer vision setting for Integrated Gradients.