# Topological structure of complex predictions

arXiv: https://arxiv.org/abs/2207.14358 · HTML: https://mlsanity.com/paper/2207.14358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 69 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [ChestX-ray8: Hospital-scale Chest X-ray Database and Benchmarks on Weakly-Supervised Classification and Localization of Common Thorax Diseases](https://mlsanity.com/paper/1705.02315/) (2017)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [CheXNet: Radiologist-Level Pneumonia Detection on Chest X-Rays with Deep Learning](https://mlsanity.com/paper/1711.05225/) (2017)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [U2-Net: Going Deeper with Nested U-Structure for Salient Object Detection](https://mlsanity.com/paper/2005.09007/) (2020)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [VOLO: Vision Outlooker for Visual Recognition](https://mlsanity.com/paper/2106.13112/) (2021)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [PageRank beyond the Web](https://mlsanity.com/paper/1407.5107/) (2014)
- [Visual Instance Retrieval with Deep Convolutional Networks](https://mlsanity.com/paper/1412.6574/) (2014)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [Deep Graph Mapper: Seeing Graphs through the Neural Lens](https://mlsanity.com/paper/2002.03864/) (2020)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [Deep Learning for Distinguishing Normal versus Abnormal Chest Radiographs and Generalization to Unseen Diseases](https://mlsanity.com/paper/2010.11375/) (2020)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)

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

- [Efficiently Learning Branching Networks for Multitask Algorithmic Reasoning](https://mlsanity.com/paper/2512.01113/) (2025)

## Abstract (arXiv)

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into pictures representing a topological view. The result is a map of the predictions that enables inspection. The methods scale up to large datasets across different domains and enable us to detect labeling errors in training data, understand generalization in image classification, and inspect predictions of likely pathogenic mutations in the BRCA1 gene.