What Do Sparse Autoencoder Feature Discovery Scores Identify? From Activations to Interventions

Abstract

Sparse autoencoder (SAE) features are typically discovered from how their activations co-vary with behaviour, yet they are often used through interventions such as steering or ablation. We take intervention attribution, the first-order effect of a specified intervention on the model output, as our estimand. For a broad class of response functions, we show that observational feature-discovery evidence generally does not identify this attribution, and derive an exact gradient-based decomposition of the gap between linear-probe predictions and intervention attribution. Across four model-SAE pairs, median probe-to-attribution magnitude ratios range from tens to hundreds, while attributions closely track small-step steering. For single-latent ablations with nonzero effects, gradient predictions match the realized sign in 91-97% of cases, compared with 17-35% for probe-implied changes. Attribution-selected sets also produce larger absolute mean ablation effects on held-out prompts than sets selected by correlation, rank tests or probe coefficients. Together, these results establish intervention attribution as a principled, gradient-estimable target for selecting SAE features for intervention.