We consider the empirical distribution of the embeddings of a k-layer polynomial GNN on a semi-supervised node classification task and prove a central limit theorem for them.

The main result is informally presented here.

Sparse autoencoders (SAEs) have recently become central tools for interpretability, leveraging dictionary learning principles to extract sparse, interpretable features from neural representations whose underlying structure is typically unknown. This paper evaluates SAEs in a controlled setting using MNIST, which reveals that current shallow architectures implicitly rely on a quasi-orthogonality assumption that limits the ability to extract correlated features. To move beyond this, we compare them with an iterative SAE that unrolls Matching Pursuit (MP-SAE), enabling the residual-guided extraction of correlated features that arise in hierarchical settings such as handwritten digit generation while guaranteeing monotonic improvement of the reconstruction as more atoms are selected.

Our model is one of the simplest possible that studies specialization in the supply-side marketplace. First, the infinite, high-dimensional content embedding space captures that digital goods can't be cleanly clustered into categories, but rather, are often mixtures of different dimensions (e.g. a movie can be both a drama and a comedy). See Anderson et al. [ 1992 ] for a textbook treatment. The assumption that all producers share the same cost function is also simplifying, but, potentially surprisingly, still allows us to study specialization. Proposition 4. F or any set of users and any 1, a pure strategy equilibrium does not exist.