Gutiérrez-Fandiño et al.'s persistence-diagram-distance method subsamples nothing — it builds the simplicial complex from every neuron and connection

Gutiérrez-Fandiño, Pérez-Fernández, Armengol-Estapé & Villegas (claim-gutierrez-fandino-2021-persistence-diagram-distance-tracks-generalization) build their simplicial complex from the complete weighted, directed graph of the network at each training batch: "For every training state, neural network connections are considered as directed and weighted edges between neurons, represented by graph nodes." Their own stated limitation is explicit that no node- or weight-level subsampling occurs anywhere in the pipeline — "we do not simplify the graph representation of the neural networks (we keep every single neuron and connections) and we do not approximate any computation." The cost they name for this choice is compute (seven days on an HPC machine), flagged as the method's "main limitation" — a scalability problem, not a selection-bias one.

Because there is no node-selection step anywhere in this method's design, a hub-selection-style artifact — where which nodes get sampled shifts the sign of an inferred signal, as in claim-hub-selection-artifact-can-reverse-network-breakpoint-signal — has no point of entry. The method reads the whole network every time, in direct contrast to the Byzantine trade-network study, whose network is too large to use in full and must be subsampled by some rule.

See observation-hub-selection-artifact-absent-by-design-in-founding-ph-generalization-papers for the synthesis across both founding NN-PH diagnostics, answering question-tda-neural-net-sampling-artifact-risk for the two papers it named.