Characterization of topological structures in different neural network architectures

TL;DR

This paper applies Topological Data Analysis (TDA) to compare neural representations across different architectures, revealing structural similarities, differences, and the impact of training stages on topology.

Contribution

It develops TDA-based methods for analyzing neural network representations and provides insights into how architecture and training influence topological structures.

Findings

Models with similar architectures have similar topologies.

Larger models exhibit smoother topological changes across layers.

Pre-trained and fine-tuned models diverge in later layers.

Abstract

One of the most crucial tasks in the future will be to understand what is going on in neural networks, as they will become even more powerful and widely deployed. This work aims to use TDA methods to analyze neural representations. We develop methods for analyzing representations from different architectures and check how one should use them to obtain valid results. Our findings indicate that removing outliers does not have much impact on the results and that we should compare representations with the same number of elements. We applied these methods for ResNet, VGG19, and ViT architectures and found substantial differences along with some similarities. Additionally, we determined that models with similar architecture tend to have a similar topology of representations and models with a larger number of layers change their topology more smoothly. Furthermore, we found that the topology of pre-trained and finetuned models starts to differ in the middle and final layers while remaining quite similar in the initial layers. These findings demonstrate the efficacy of TDA in the analysis of neural network behavior.