The ladder of decomposition baselines

Members — a guided walk

1. Default (neuron/residual-stream) basis baseline

   The ladder of baselines starts with the most literal hypothesis about where a model's features live: the default basis baseline, treating individual neurons, or for the residual stream individual coordinates, as the units worth scoring directly. It is shown, via the apostrophe-dimension case study, to be polysemantic exactly where the corresponding learned dictionary feature is monosemantic, and every stronger baseline in this theme is an attempt to do better than this naive starting point. The weakest possible alternative to it is not a smarter basis at all, but no basis, just random directions.

2. Random directions baseline

   The random directions baseline samples directions in activation space with no relationship to the model's computation whatsoever, a lower bound against which the default basis, PCA, and ICA are all compared in the paper's autointerpretability figures. If a learned dictionary scored no better than random directions, sparsity-driven decomposition would have nothing to recommend it; the next two baselines instead ask whether some principled, non-random criterion for choosing directions can close that gap.

3. Principal Component Analysis (PCA)

   Principal Component Analysis chooses directions of maximal variance in the activation data, the paper's first non-arbitrary baseline decomposition, run online on the same quantity of data used to train the autoencoders. PCA underperforms the learned dictionaries both on autointerpretability score and, in Section 4, on IOI-patching precision, where it needs more patched features and larger edit magnitudes to reach the same KL divergence from target. A different, sparsity-adjacent principle does better than maximizing variance: maximizing statistical independence.

4. Independent Component Analysis (ICA)

   Independent Component Analysis finds statistically independent, maximally non-Gaussian directions, and it is consistently the strongest of the four baselines, on both metrics the paper runs. The paper's kurtosis and skew analysis explains why: interpretability correlates weakly but positively with how heavy-tailed a feature's activations are, and ICA is the one baseline built to directly optimize for exactly that non-Gaussian, heavy-tailed property. Because ICA and PCA both activate across an entire half-space rather than only past a threshold like the SAE does, the paper subjects them to one further check before declaring the comparison fair.

5. Top-K-active baseline control

   The top-K-active baseline control, in Appendix G, restricts PCA and ICA to a fixed number K of simultaneously active directions per datapoint, matched to the sparse autoencoder's own average active-feature count at R=1 and alpha=8.6e-4. This tightens the ladder by removing a structural advantage the SAE might otherwise have simply by activating fewer directions per input at once, and the adjustment is found to explain only a small fraction of the interpretability gap. With every rung of the ladder handicapped as fairly as the paper can manage, what remains standing above all four baselines is the sparse autoencoder itself.

6. Sparse autoencoders (SAEs)

   Sparse autoencoders are what every one of these baselines is run against, on both of the paper's central comparisons: autointerpretability score and IOI-patching precision alike. Beating the default basis rules out neurons as the right unit, beating random directions rules out that any direction would do, and beating PCA and even the tightened, top-K-matched ICA rules out variance-maximization and non-Gaussianity-maximization as sufficient substitutes for what sparsity-driven dictionary learning finds. The ladder is how Cunningham et al. (2023) argue that sparse autoencoders recover something more specific than any generic statistical decomposition of activation space -- a claim earned one baseline at a time.

Superthemes

• Decomposing the model into features

Edges explored within this theme

• Default (neuron/residual-stream) basis baseline — loses to → Sparse autoencoders (SAEs)
• Principal Component Analysis (PCA) — trails → Sparse autoencoders (SAEs)
• Independent Component Analysis (ICA) — converges with → Sparse autoencoders (SAEs)
• Random directions baseline — anchors → Autointerpretability score
• Top-K-active baseline control — density matches → Independent Component Analysis (ICA)
• Principal Component Analysis (PCA) — gets more training data than → Independent Component Analysis (ICA)

Super edges touching this theme

• The ladder of decomposition baselines — ranks every rung through → Interpretability itself becomes a benchmark

Sources

Every passage behind this theme’s member concepts.