Filan et al. (2020) — ARXIV-2003.04881
Key takeaways
- Makes “is this network modular?” answerable by importing the definition from graph clustering — a module is neurons with strong internal and weak external connectivity — and measuring it by spectral clustering the weight graph of an MLP
- The control is the paper. Pruned networks are sparse, and sparse graphs cluster more easily, so the comparison that matters is against random networks with the same sparse weight distribution — and trained+pruned MLPs are significantly more modular than those too
- Networks trained with dropout are much more modular — a regulariser with a measurable structural consequence, not only a generalisation one
- Small MLPs on small images, with notable spread in the n-cut values on CIFAR-10
Standing in the anthology
Read — NOTE-061. The document is Superseded, correctly: interpretability
moved to mechanistic circuit-level work on transformers, and a connectivity
statistic on pruned MLPs is not where it went.
Two of the four takeaways asserted results the paper does not contain. “Feature disentanglement” is not measured — the paper measures connectivity, not features — and “impact on generalization” is not studied at all; no generalization claim appears anywhere in it.
What survives is the methodological move: when an intervention produces a structural property, control against a random baseline matched on the intervention’s incidental statistics, not only against the pre-intervention one. Structural claims about networks routinely omit that control.