Intrinsic-Dimension-Guided Bottleneck Selection for Variational Autoencoders with Active-Unit Diagnostics

Intrinsic-dimension (ID) estimates and active-unit diagnostics address different aspects of variational-autoencoder bottleneck selection. We evaluate search policies on four image datasets, five training seeds and five regularisation weights under explicit validation targets and common candidate costs. Holding reliability checks, fallback and reference charges fixed, ID is accepted only for 25 MNIST conditions. ID-derived and gated midpoint starts select identical widths, requesting 8.84 and 5.84 candidates on average; the other 75 conditions share an ascending fallback. In 10,000 coefficient–threshold replay evaluations, 155 local outputs miss the smallest qualifying width. A separate five-seed MNIST study adds Monte Carlo evidence-lower-bound capacity selection. Native pruning experiments distinguish full-model reconstruction, selected-axis masking, decoder adaptation and dimension transfer. On dSprites, zero-centred relevance-prior masking increases MSE by a mean seed-wise 128.6%; after equal additional decoder training, the unmasked model meets the quality target in all three seeds whereas the masked model remains 60.9% worse and fails it. Active-unit prediction establishes no additional benefit on its near-ceiling task. These bounded results separate representation geometry, which intrinsic dimension measures, from reconstruction-sufficient width, which also depends on objective, training budget and quality target, and support controlled evaluation of selection rules and diagnostics without a general efficiency or pruning guarantee.