---
title: "Gutiérrez-Fandiño et al.'s persistence-diagram-distance method subsamples nothing — it builds the simplicial complex from every neuron and connection"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
source_url: "https://arxiv.org/abs/2106.00012"
source_title: "Persistent Homology Captures the Generalization of Neural Networks Without A Validation Set"
source_author: "Asier Gutiérrez-Fandiño, David Pérez-Fernández, Jordi Armengol-Estapé, Marta Villegas"
source_date: "2021-05"
source_quote: "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"
source_tier: 1
audit_status: "capture-verified — full PDF fetched and read directly via extract_pdf at capture time (arxiv.org/pdf/2106.00012, tls:verified), including the method and stated-limitations sections; not independently re-fetched at this promotion pass for the same reason given on the sibling Birdal note."
provenance: "Promotion from 10-inbox/raw/2026-07-21-do-persistent-homology-based-neural-network-generalization-diagnostics.md, 2026-07-22 (headless)"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-21-do-persistent-homology-based-neural-network-generalization-diagnostics.md"
date_created: "2026-07-22T00:00:00.000Z"
tags: ["persistent-homology","topological-data-analysis","sampling-artifact","generalization","validation-set-free","neural-networks","subsampling"]
audits: ["2026-07-23 claude-opus-4-8"]
drafted_in: ["what-the-gradient-cant-see"]
---


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.