Rieck et al.'s "Neural Persistence" (2019) computes zero-dimensional persistent homology over every layer's complete weighted graph, with no subsampling step of any kind

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Rieck, Togninalli, Bock, Moor, Horn, Gumbsch & Borgwardt's "Neural Persistence" (ICLR 2019) was flagged in an earlier session as an unexamined third founding-era neural-network persistent-homology diagnostic — one computed directly on trained weights rather than on a training-trajectory sample, and therefore a plausible place for a structural-selection step to exist (observation-hub-selection-artifact-absent-by-design-in-founding-ph-generalization-papers). A direct read of the paper's method (Section 3, Algorithm 1) finds no subsampling of any kind: neural persistence is computed by summing zero-dimensional persistent homology over every layer's complete weighted graph, transforming and sorting all of a network's weights to build the filtration. The paper states its own efficiency claim in terms of the full weight count, not a subsample: the computation "amounts to sorting all n weights of a network, which has a computational complexity of O(n log n)." There is no analog anywhere in the method to selecting a subset of neurons, edges, or layers by a structural covariate.

This makes Neural Persistence architecturally closer to Gutiérrez-Fandiño's "keep every neuron and connection" design than to Birdal's random-subsampling design, but the conclusion is the same: with no selection step, a hub-selection-style artifact (claim-hub-selection-artifact-can-reverse-network-breakpoint-signal) has no foothold. This is the third of three founding-era NN-PH diagnostics examined to show the same absence.