From Geometric Recovery to Causal Validation: A Reproducible Audit of Sparse Autoencoder Features, from Superposition Geometry to Causal Inertness

Abstract

Sparse autoencoders (SAEs) are the standard for decomposing superposed neural representations into interpretable features, and evaluation relies predominantly on correlational recovery metrics -- cosine similarity between ground-truth directions and decoder atoms. We show this conflates two distinct claims: decoder-geometry alignment and encoder-activation behavior. We reproduce the superposition phase diagram of Elhage et al. (2022), identifying a convergence artifact at high sparsity and an under-described diffuse sharing regime at extreme overcompleteness. We reproduce the TopK-versus-L1 comparison of Gao et al. (2024), with direct evidence of L1 shrinkage. Our central result is causal: subjecting every recovered feature to ablation and steering, we find up to 77% of features passing a recovery bar (cosine >= 0.90) in a degraded SAE -- and 9% in a well-trained one -- are causally inert: the matched atom never fires when the feature is present, including matches at cosine ~1.000. We package the method as sae-causal-audit, a model-agnostic instrument with a deterministic pipeline. Re-auditing refines the finding: inertness decomposes by cause into structural inertness (antipodal-pair geometry, present in good SAEs) and competitive inertness (a TopK pathology of degraded SAEs), and by direction into read- and write-inertness, which five antipodal pairs dissociate completely -- unmonitorable yet steerable through the same atom, with steering specificities of 143-310 attached to zero ablation effects. We document why byte-exact reproducibility is unavailable by construction, and propose reporting it as a stack of claims with explicit scopes. Applying the instrument to a production SAE reproduces the pattern at small scale (14% inert) and surfaces an atom-collision signal: a handful of atoms recur as the nearest match for dozens of unrelated concepts, replicated across three batches.