Community structure of the pseudofractal web

What the math gives to ML

The paper provides an exactly solvable example showing that ordinary community evidence can mistake heavy-tailed degree variation for structure, while degree-corrected evidence recovers a nested hierarchy. The transferable asset is not the pseudofractal graph itself, but the model-selection principle: compare a partition against a degree-preserving null and recursively refine only when corrected evidence increases. This suggests a hierarchical router or graph pooling module whose assignments are driven by residual interaction structure rather than raw token frequency, node degree, or popularity. The strongest first test is a degree-corrected hierarchical MoE router on synthetic power-law data and a small language model, measuring whether it reduces expert collapse and improves quality at fixed communication cost.