EMNLP 2026 Tutorial · Causal Foundations for Interpretability

SAEs trained on the same activations disagree

Two seeds, two dictionaries: consistent with several sparse solutions.

Training seed seed 2 toy, computed live

	seed 1 (dashed)	seed 2 (solid)
Reconstruction error
Sparsity cost

SAE: sparse autoencoder; it rebuilds each activation from a few features, and its dictionary is the set of feature directions (the arrows).
Dots: 20 toy activations in 2-D. Seed: the random number that sets where training starts.
Reconstruction error: mean squared distance from a dot to its rebuild, 0 here because any two arrows rebuild a 2-D dot. Sparsity cost: mean summed size of the two feature values per dot; lower is sparser.