A differentiability framework for zigzag persistent homology via linear interpolation

Excerpt

arXiv:2609.39242v1 Announce Type: new Abstract: Persistent homology can be differentiated and incorporated into learning pipelines, but no analogous framework exists for zigzag persistence, which is needed when the underlying topological structure evolves non-monotonically over time. We develop such a framework for sequences of simplicial complexes obtained by thresholding time-dependent filtering values on a fixed complex. By assigning persistence diagram endpoints the real-valued times at whic