# Barcodes as Summary of Loss Function Topology

arXiv: https://arxiv.org/abs/1912.00043 · HTML: https://mlsanity.com/paper/1912.00043/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2019.

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

- [Scalar Function Topology Divergence: Comparing Topology of 3D Objects](https://mlsanity.com/paper/2407.08364/) (2024)

## Abstract (arXiv)

We propose to study neural networks' loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes to explore topology of loss surfaces. An algorithm for calculations of the loss function's barcodes of local minima is described. We have conducted experiments for calculating barcodes of local minima for benchmark functions and for loss surfaces of small neural networks. Our experiments confirm our two principal observations for neural networks' loss surfaces. First, the barcodes of local minima are located in a small lower part of the range of values of neural networks' loss function. Secondly, increase of the neural network's depth and width lowers the barcodes of local minima. This has some natural implications for the neural network's learning and for its generalization properties.