  We propose an approach to learning with graph-structured data in the problem
domain of graph classification. In particular, we present a novel type of
readout operation to aggregate node features into a graph-level representation.
To this end, we leverage persistent homology computed via a real-valued,
learnable, filter function. We establish the theoretical foundation for
differentiating through the persistent homology computation. Empirically, we
show that this type of readout operation compares favorably to previous
techniques, especially when the graph connectivity structure is informative for
the learning problem.
