Complexity and Stability of Neural Activity Across Aging and Neurodegenerative Disease

What the math gives to ML

The paper provides a robust, distribution-level notion of representation complexity based on how many metric balls cover almost all probability mass. This is transferable to neural networks as a scale-dependent intrinsic-dimension regularizer that tolerates a controlled fraction of atypical examples, unlike simple variance or rank penalties. The most practical implementation is a differentiable soft approximation to the measure covering number applied to hidden embeddings, combined with an anti-collapse constraint and evaluated through held-out covering complexity, accuracy, and activation compression.