The hump-shaped ID profile is likely a TwoNN estimator artifact

Schulte & Rugamer prove that standard network layers (linear/conv, ReLU, softmax, pooling, residual, normalization, self-attention) are Lipschitz maps, so true pointwise and Hausdorff intrinsic dimension can only stay equal or decrease across a layer, never increase [schulte-rugamer-2026-rethinking-intrinsic-dimension-estimation] Yet the standard TwoNN/MLE/GRIDE pipeline on ResNet-34, Llama-3.1-8B, Mistral-7B-v0.3, and Pythia-6.9B reproduces the familiar hump-shaped expansion-then-compression ID profile, a pattern their theorem proves cannot be the true ID [schulte-rugamer-2026-rethinking-intrinsic-dimension-estimation] Investigating what the estimators actually respond to (neighbor distances, ambient dimension, cosine similarity, norm, entropy), they conclude the mid-layer-ID-peak abstraction narrative is very likely a systematic estimator artifact [schulte-rugamer-2026-rethinking-intrinsic-dimension-estimation] The caution applies specifically to TwoNN and related nearest-neighbor-ratio estimators, not to MST-based, spectral-entropy/effective-rank, or SVD-based measures [schulte-rugamer-2026-rethinking-intrinsic-dimension-estimation]