---
title: "Neural Persistence"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Neural Persistence"
aliases: []
first_seen: "2026-07-21T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["persistent homology","Bastian Rieck","Karsten Borgwardt","persistent homology dimension (PHD)","generalization (neural networks)"]
seek_code_commit: "850b81d"
---


A complexity measure introduced by Rieck, Togninalli, Bock, Moor, Horn,
Gumbsch & Borgwardt (ICLR 2019) that scores a trained neural network by
running zero-dimensional persistent homology over each layer's complete
weighted graph, transforming and sorting every weight to build the
filtration — computed once, directly on trained weights, rather than
tracked across a training trajectory. The third founding-era
neural-network persistent-homology diagnostic examined in this vault's
cluster, architecturally distinct from both
[[entity-tolga-birdal|Birdal's]] (random-sampling-over-time) and
[[entity-asier-gutierrez-fandino|Gutiérrez-Fandiño's]] (no-sampling,
full-network-every-step) constructions, yet sharing their absence of any
structural-selection step.

## References
- [[claim-rieck-2019-neural-persistence-computed-without-subsampling]]
- [[observation-hub-selection-risk-needs-incomplete-object-nn-diagnostics-read-complete-record]]
- [[entity-bastian-rieck]] · [[entity-persistent-homology-dimension]]