Anytime-Valid Hypothesis Testing for Sparse Autoencoder Feature Validation

Sparse autoencoders have become a standard tool for interpreting the internal representations of neural language models, but feature validation remains largely correlational and ad hoc. We introduce a sequential, anytime-valid hypothesis testing framework for validating SAE features against a causal necessity criterion. For each candidate feature, we construct an e-process from paired ablation interventions; across large feature dictionaries, we control the false discovery rate using the e-BH procedure, which is valid under arbitrary dependence between feature-level e-values, and which lets researchers stop at any sample size without inflating Type-I error. On a synthetic task with oracle ground truth, our procedure controls FDR below the target level (empirical FDP $= 0.000 \pm 0.000$ across 10 seeds at $\alpha = 0.05$) while recovering features in proportion to their causal effect size. On GPT-2 small with publicly available residual-stream SAEs, our procedure recovers six features on the indirect object identification benchmark at $\alpha = 0.05$ from $K = 89$ candidates, while Model-X knockoffs with a Gaussian fit recover none on the same data; five of the six recovered features have published interpretations directly aligned with the task structure.