A Perturbation Ladder for Sparse Autoencoder Dictionaries: Seed, Optimizer and Precision Against a Measured Baseline

Measures how much of a TopK sparse autoencoder's learned dictionary survives three perturbations - random seed, optimizer, and weight precision - using one matching procedure and one calibration so the three are comparable. Two autoencoders differing only in seed agree on 8.3-9.1% of matchable features (Pearson) across three pairwise comparisons at over 100x a permutation null. Against that baseline, changing the optimizer separates (intervals disjoint) while 4-bit quantisation does not (intervals overlap), so on this model and layer interpretability on quantised weights costs no more than the sampling variance of training a single autoencoder. Muon reaches equal-or-better reconstruction with 23x fewer dead features at 6.5x the wall clock, and dictionary collapse fires at the same step under both optimizers while only Muon recovers. All runs on a single Apple M1 Max.