Sparse autoencoder features get a ground-truth ruler: seed reproducibility is not concept alignment, and a five-seed consensus reaches 78–98%

Judging whether SAE features can be trusted requires separating cross-seed reproducibility from concept coverage and gene-program purity, because the two rank methods in opposite orders on every embedding tested. Reproducibility across seeds had served as the main test of feature trust, and dedicated methods raise it through aligned training, archetypal constraints or pooling across seeds. Across five spatial transcriptomics embeddings, Geneformer embeddings, synthetic data with planted programs and the Pythia-70m residual stream, single SAE fits reproduced only 27–46% of their features, whereas varimax rotations reproduced 99–100% on every source yet covered at most one concept on any biological or text embedding.

A consensus over five SAE fits with different seeds isolates features that recur, so each retained feature can be interpreted with confidence. Features of a single fit largely fail to reappear when the method is refitted on the other half of the cells, while the consensus raised reproducibility to 92–98% on the spatial embeddings, 89–95% on planted data, 85% on Geneformer and 78% on the language model. Consensus features were as pure as single-fit features: chimeric features made up 11–40% of the consensus, against 44–70% for varimax and 46–69% for sparse varimax, and the consensus was purer than every rotation on all five spatial embeddings.

The consensus gain carries a stated cost: it keeps the strong concepts shared across seeds and discards mostly seed-specific detail. Compared with single fits, the consensus covered fewer lineages on three of five spatial embeddings, a median of 1.0 fewer, and kept 7–64% of their concept-specific features. On planted data at sequencing depth 500, single fits recovered 0.89, 0.33 and 0.17 of the strong, mid and weak states, the consensus 1.00, 0.67 and 0.28, and varimax 1.00, 0.94 and 0.61; neither a 15,000-step single fit nor a second SAE trained on the consensus residual recovered what was discarded.

The conclusions rest on embeddings whose concepts are known: five spatial embeddings from two colorectal cancer CosMx sections, Geneformer V2 single-cell embeddings, synthetic data with planted programs, and rule-defined token classes on the layer-3 residual stream of Pythia-70m. The authors note that a state an embedding does not carry cannot be evaluated on this ground truth, and that two SAE variants and models of up to 70 million parameters were tested.

The authors describe the ground truth as narrow, limited to lineages, planted programs and rule-defined token classes, and tested only two SAE variants, models of up to 70 million parameters and two spatial sections from one cancer type. Reproducibility itself varies with embedding geometry and data volume: the language-model embedding spreads its variance over about 70 effective dimensions and token classes explain only 12% of it, giving 78% consensus reproducibility against 85–98% on biological embeddings. The authors propose removing dominant variance before fitting, for example by fitting within lineages, as a more direct route to weak states, and state that they did not test it.