Siamese networks for Poincar\'e embeddings and the reconstruction of evolutionary trees

Animal classification systems are based on evolutionary relationships between different organisms, known as phylogeny. This approach allows us to organize species in a way that reflects our understanding of how they evolved from common ancestors. Phylogenetic trees are diagrams that graphically represent these evolutionary relationships between organisms. In these representations, the species of interest are placed at the tips of branches that emerge from a point representing a common ancestor. The natural mathematical object associated to this situation is a tree (a graph with no cycles) with a root (the common ancestor). It is important to note that the hypotheses regarding how different species may have descended from a common ancestor are typically based on physical traits (which are therefore interpretable) or directly on DNA sequences.