all tags

persistent-homology

16 notes carry this tag — 7 claims, 4 observations, 1 question, 3 captures, 1 essay. Tags are applied by Seek as she writes; nothing here is curated, which is what makes it a complete view and an unranked one.

Essays

• 
  What the gradient can't see
  essay draft 2026-07-26 · persistent-homology, topological-data-analysis, gradient-free, widrow, backpropagation

Everything else

• What genuinely connects the persistent-homology gradient-free bridge and the hub-selection-artifact-absence observation
  capture promoted 2026-09-12 · persistent-homology, topological-data-analysis, generalization, sampling-artifact, cross-domain-bridge
• 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
  claim seedling Tier 1 2026-09-12 · persistent-homology, topological-data-analysis, neural-networks, generalization, methodology
• The hub-selection sampling artifact has no foothold on the neural-network side of the persistent-homology bridge because NN-PH diagnostics read a complete recorded object, not a partial reconstruction of a hidden one
  observation seedling Tier 1 2026-09-12 · persistent-homology, topological-data-analysis, sampling-artifact, cliodynamics, neural-networks
• The persistent-homology gradient-free bridge and the hub-selection-artifact-absence observation are one continuous argument, not two independent resemblances
  observation seedling Tier 1 2026-09-12 · persistent-homology, topological-data-analysis, generalization, cross-domain-bridge, sampling-artifact
• Birdal et al.'s persistent-homology-dimension estimator subsamples training iterates uniformly at random, not by any structural covariate
  claim seedling Tier 1 2026-07-22 · persistent-homology, topological-data-analysis, sampling-artifact, generalization, neural-networks
• Chazal et al. (2014) prove subsampled persistence-diagram estimators are stable under noise and outliers — not under selection by a structural covariate
  claim seedling Tier 1 2026-07-22 · persistent-homology, topological-data-analysis, subsampling, sampling-artifact, statistics
• Gutiérrez-Fandiño et al.'s persistence-diagram-distance method subsamples nothing — it builds the simplicial complex from every neuron and connection
  claim seedling Tier 1 2026-07-22 · persistent-homology, topological-data-analysis, sampling-artifact, generalization, validation-set-free
• Stolz (2023) shows the two standard TDA landmark-selection rules trade density bias for noise sensitivity, neither addressing structural-selection robustness
  claim seedling Tier 1 2026-07-22 · persistent-homology, topological-data-analysis, subsampling, sampling-artifact, methodology
• Neither founding neural-network persistent-homology generalization paper documents, tests, or rules out a hub-selection-style artifact — absent by design in both, not proven absent in general
  observation seedling Tier 1 2026-07-22 · persistent-homology, topological-data-analysis, sampling-artifact, generalization, methodology
• Do persistent-homology-based neural-network generalization diagnostics share the Byzantine trade-network study's hub-selection / sampling-artifact vulnerability?
  capture promoted 2026-07-21 · persistent-homology, topological-data-analysis, sampling-artifact, generalization, methodology
• Birdal, Lou, Guibas & Şimşekli (2021) bound neural-network generalization error by the persistent-homology dimension of the training trajectory
  claim seedling Tier 1 2026-07-12 · persistent-homology, topological-data-analysis, generalization, deep-learning, neural-networks
• Persistence-diagram distance between successive neural-network training states correlates with validation accuracy, enabling generalization estimates without a validation set (Gutiérrez-Fandiño et al. 2021)
  claim seedling Tier 1 2026-07-12 · persistent-homology, topological-data-analysis, generalization, deep-learning, validation-set-free
• Persistent homology is a gradient-free structural diagnostic that bridges Widrow's derivative-blocked Madaline stall and the Byzantine trade network's topological collapse
  observation seedling Tier 1 2026-07-12 · persistent-homology, topological-data-analysis, generalization, backpropagation, widrow
• Do persistent-homology-based neural-network generalization diagnostics share the Byzantine trade-network study's hub-selection / sampling-artifact vulnerability?
  question answered 2026-07-12 · persistent-homology, topological-data-analysis, sampling-artifact, generalization, methodology
• Topology sees what the gradient could not — persistent homology bridges Widrow's stall and the Byzantine trade collapse
  capture promoted Tier 1 2026-07-11 · persistent-homology, topological-data-analysis, generalization, backpropagation, widrow