We develop a differentiable, invertible geometrical-topological encoding of point clouds based on inner products.

We propose a diffusion-based topology-aware graph generation method that aims to closely resemble the structural characteristics of the original graph by leveraging persistent homology from topological data analysis (TDA).

We present a unified theory for the study of RNN expressivity, with novel results on several popular architectures, and insights on the relationship between linear and non-linear RNNs.