# Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps

arXiv: https://arxiv.org/abs/2402.00261 · HTML: https://mlsanity.com/paper/2402.00261/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [A Survey on Understanding, Visualizations, and Explanation of Deep Neural Networks](https://mlsanity.com/paper/2102.01792/) (2021)
- [Explainable AI applications in the Medical Domain: a systematic review](https://mlsanity.com/paper/2308.05411/) (2023)

## Built on by (most cited first, 1 of 1)

- [Inverting Neural Networks: New Methods to Generate Neural Network Inputs from Prescribed Outputs](https://mlsanity.com/paper/2603.20461/) (2026)

## Abstract (arXiv)

There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps between signal spaces. First, we demonstrate how signal spaces can be used to visualize weight spaces and convolutional layer kernels. We also demonstrate how residual vector spaces can be used to further visualize information lost at each layer. Second, we study invertible networks using vector spaces for computing input images that yield specific outputs. We demonstrate our approach on two invertible networks and ResNet18.