Language, trees, and geometry in neural networks

Any two Pythagorean embeddings of the same tree are isometric—and related by a rotation or reflection—since distances between all pairs of points are the same in both. Any weighted tree with $n$ nodes has a Pythagorean embedding into $\mathbb{R}^{n-1}$. In other words, in a space that is sufficiently high-dimensional, a randomly branching embedding of a tree, where each child is offset from its parent by a random unit Gaussian vector, will be approximately Pythagorean.

Source: pair-code.github.io