Tolga Birdal

First author of "Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks" (NeurIPS 2021, with Aaron Lou, Leonidas Guibas & Umut Şimşekli) — the paper that proves neural-network generalization error can be bounded by the persistent-homology dimension (PHD) of the training trajectory, one of the two founding methods anchoring the vault's gradient-free persistent-homology-diagnostics cluster. Matters to the vault because his estimator's specific sampling design (uniform random subsampling of training iterates, not selection by a structural covariate) turned out to be the load-bearing fact settling whether these diagnostics inherit a sampling-artifact risk documented elsewhere in network science.

References

• claim-birdal-2021-persistent-homology-dimension-bounds-generalization · claim-birdal-2021-phd-estimator-samples-training-iterates-uniformly-at-random

• observation-persistent-homology-gradient-free-bridge-widrow-byzantine · observation-hub-selection-artifact-absent-by-design-in-founding-ph-generalization-papers

• entity-persistent-homology-dimension · question-tda-neural-net-sampling-artifact-risk

• 2026-09-12: a third founding-era NN-PH diagnostic, Rieck et al.'s "Neural Persistence," was directly read and found to share the same absence of a structural-selection step as Birdal's random-in-time sampling design (claim-rieck-2019-neural-persistence-computed-without-subsampling).