# Topology-based Representative Datasets to Reduce Neural Network Training Resources

arXiv: https://arxiv.org/abs/1903.08519 · HTML: https://mlsanity.com/paper/1903.08519/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2019.

## Built on by (most cited first, 6 of 6)

- [Singular value decomposition based matrix surgery](https://mlsanity.com/paper/2302.11446/) (2023)
- [Trainable and Explainable Simplicial Map Neural Networks](https://mlsanity.com/paper/2306.00010/) (2023)
- [Importance attribution in neural networks by means of persistence landscapes of time series](https://mlsanity.com/paper/2302.03132/) (2023)
- [An In-Depth Analysis of Data Reduction Methods for Sustainable Deep Learning](https://mlsanity.com/paper/2403.15150/) (2024)
- [Topological Quality of Subsets via Persistence Matching Diagrams](https://mlsanity.com/paper/2306.02411/) (2023)
- [Application of the representative measure approach to assess the reliability of decision trees in dealing with unseen vehicle collision data](https://mlsanity.com/paper/2404.09541/) (2024)

## Abstract (arXiv)

One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. These changes are driven by a dataset, which can be seen as a set of labelled points in an n-dimensional space. In this paper, we explore the concept of are representative dataset which is a dataset smaller than the original one, satisfying a nearness condition independent of isometric transformations. Representativeness is measured using persistence diagrams (a computational topology tool) due to its computational efficiency. We prove that the accuracy of the learning process of a neural network on a representative dataset is "similar" to the accuracy on the original dataset when the neural network architecture is a perceptron and the loss function is the mean squared error. These theoretical results accompanied by experimentation open a door to reducing the size of the dataset to gain time in the training process of any neural network.