The Attribution Impossibility: No Feature Ranking Is Faithful, Stable, and Complete Under Collinearity
No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) fo...
| Authors | Drake Caraker, Bryan Arnold, David Rhoads |
|---|---|
| Primary category | cs.LG |
| Published | 8 April 2026 |
| Last updated at source | 8 April 2026 |
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