Sparse Autoencoder Attribution Graphs Are Decided at the Margin

Attribution graphs over the features of sparse autoencoders (SAEs) are used to predict what an ablation does and are compared across training seeds. A TopK SAE keeps the largest preactivations at each token, and a feature's margin is its preactivation's distance to the cutoff. On five public TopK SAE pairs from three Pythia models, zeroing one feature moves a next layer feature across the cutoff in 0.74 of cases or more, and the crossings carry most of the response's energy. Over writes that scale a feature's code by three factors, the graph built on the features active beforehand has a median relative error of 0.247 or more. The margin graph adds the first order change to every preactivation and reranks, at the same cost, and errs by at most 0.033. At the median, the crossing features' decoded change is 1.24 times the model's own change in norm or more. Between seeds of one testbed, sparse maps between features explain 0.85 of a graph's energy on its active features, and 0.47 once the other seed's graph keeps only its own. The largest model studied is pythia-160m.