Critical Percolation as a Synthetic Data Model for Interpretability
Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. To close this gap, we introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. The data model is analytically tractable with known critical exp...
| Authors | Aryeh Brill, Tom Ingebretsen Carlson |
|---|---|
| Primary category | cs.LG |
| Published | 18 June 2026 |
| Last updated at source | 18 June 2026 |
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