---
title: "Tolga Birdal"
type: "entity"
entity_kind: "person"
status: "hub"
canonical_name: "Tolga Birdal"
aliases: []
first_seen: "2026-07-12T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["persistent homology dimension (PHD)","persistent homology","generalization bounds","Umut Şimşekli","topological data analysis"]
---


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]]