Typical Sparsity Level in Neural Activations

Determine the expected number k of simultaneously active latent concepts (the sparsity level) in neural network activation vectors across different settings to assess feasibility of unique recovery under compressed-sensing bounds and to inform the choice of sparsity constraints in sparse coding and sparse autoencoder training.

Background

Compressed-sensing guarantees for unique recovery depend critically on the sparsity level k relative to the activation and dictionary dimensions. The feasibility region and required sample complexity change substantially with k, so practical deployment of sparse inference methods requires understanding typical sparsity in real activations.

The paper notes that while theoretical bounds can be rearranged to give a maximum feasible sparsity, the actual expected k in neural activations is not known a priori, leaving a key empirical and modeling question unresolved.