  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.
