Why Scalar Interaction Scores Fail: Stochastic Hi-Fi Recovers 411x Larger Structures

Signed pairwise interaction scores fundamentally conflate uniqueness (U), redundancy (R), and synergy (S). A new paper proves this on a minimal 3-way XOR structural causal model: faithful indices like Shapley-Taylor return zero per pair, while projective indices like Shapley Interaction spread the third-order effect into scalars that mix all three mechanisms.

Stochastic Hi-Fi: Interventional Decomposition Without Retraining

The authors introduce Stochastic Hi-Fi, a post-hoc predictability decomposition that estimates per-feature U/R/S profiles using interventional masked inference. It provides exact interventional semantics, finite-sample Monte Carlo bounds, strict variance reduction from coupled diamond sampling, and uniform finite-vocabulary convergence. No retraining required.

411x Recovery Ratios and Real-World Circuits

Across tabular SCMs, Stochastic Hi-Fi recovers structure missed by scalar baselines with up to 411x larger interaction-magnitude recovery ratios. On GPT-2's IOI circuit, it separates redundant and synergistic attention heads. On NIH ChestX-ray14, Stochastic Hi-Fi matches GradCAM on Pointing Game and improves substantially on Deletion AUC.

Stochastic Hi-Fi gives researchers a tool to decompose interactions into irreducible components, moving beyond scalar summaries toward faithful interpretability.

Source: The Representational Limit of Scalar Interactions: An Interventional Decomposition
Domain: arxiv.org