Fundamental Limits of Neural Network Sparsification: Evidence from Catastrophic Interpretability Collapse

Abstract: Extreme neural network sparsification (90% activation reduction) presents a critical challenge for mechanistic interpretability: understanding whether interpretable features survive aggressive compression. This work investigates feature survival under severe capacity constraints in hybrid Variational Autoencoder--Sparse Autoencoder (VAE-SAE) architectures. We introduce an adaptive sparsity scheduling framework that progressively reduces active neurons from 500 to 50 over 50 training epochs, and provide empirical evidence for fundamental limits of the sparsification-interpretability relationship. Testing across two benchmark datasets -- dSprites and Shapes3D -- with both Top-k and L1 sparsification methods, our key finding reveals a pervasive paradox: while global representation quality (measured by Mutual Information Gap) remains stable, local feature interpretability collapses systematically. Under Top-k sparsification, dead neuron rates reach $34.4\pm0.9\%$ on dSprites and $62.7\pm1.3\%$ on Shapes3D at k=50. L1 regularization -- a fundamentally different "soft constraint" paradigm -- produces equal or worse collapse: $41.7\pm4.4\%$ on dSprites and $90.6\pm0.5\%$ on Shapes3D. Extended training for 100 additional epochs fails to recover dead neurons, and the collapse pattern is robust across all tested threshold definitions. Critically, the collapse scales with dataset complexity: Shapes3D (RGB, 6 factors) shows $1.8\times$ more dead neurons than dSprites (grayscale, 5 factors) under Top-k and $2.2\times$ under L1. These findings establish that interpretability collapse under sparsification is intrinsic to the compression process rather than an artifact of any particular algorithm, training duration, or threshold choice.