Independent Component Analysis (ICA)
Sparse Autoencoders Find Highly Interpretable Features in Language Models — inherited
A standard technique that finds maximally non-Gaussian (statistically independent) directions in data, used as a baseline decomposition of model activations. ICA is consistently the strongest of the non-dictionary-learning baselines, which the paper attributes to interpretability correlating with activation kurtosis and skew -- properties ICA directly optimizes for.
Of several older techniques for finding structure in a network's internal activations, one keeps closing the gap against a newer method in a way the others don't — a decades-old signal-processing trick with no history in language models at all, originally built to separate overlapping voices in an audio recording. That it performs unusually well turns out not to be a coincidence: what it optimizes for and what makes a feature interpretable line up more closely than expected.
The page covers what this technique does mathematically, why maximizing non-Gaussianity tracks the same statistical signature that predicts interpretability elsewhere in the paper, and where its advantage holds up against the newer method — and where, deeper into the network, it closes the gap almost entirely.
The one baseline that keeps pace
Among the four baseline decompositions this paper measures against its sparse dictionaries -- the Default (neuron/residual-stream) basis baseline, the Random directions baseline, Principal Component Analysis (PCA), and ICA -- Independent Component Analysis is consistently the strongest non-learned competitor on the Autointerpretability score (sparse-autoencoders, §"3.2 SPARSE DICTIONARY FEATURES ARE MORE INTERPRETABLE THAN BASELINES", p. 3). It is old enough and general enough to need no introduction specific to this paper: ICA predates sparse autoencoders by decades and is used across signal processing and neuroscience for problems with no connection to language models.
Finding sources that don't look Gaussian
ICA is a classical blind source separation technique (formalized by Comon, 1994): given observed mixtures $x = As$ of unknown, statistically independent source signals $s$, it recovers an unmixing matrix $W \approx A^{-1}$ without knowing $A$ or $s$ in advance -- the textbook example is separating individual voices from overlapping microphone recordings at a cocktail party. What makes this possible is a fact about Gaussian variables: linear mixtures of independent non-Gaussian sources become more Gaussian than the sources themselves, by a version of the central limit theorem, so ICA works by searching for the projection that is maximally non-Gaussian, typically via a proxy such as negentropy or kurtosis -- algorithms like FastICA (Hyvärinen, 1999) iteratively maximize a contrast function $J(w) \propto \big(\mathbb{E}[G(w^\top x)] - \mathbb{E}[G(\nu)]\big)^2$ for a nonquadratic $G$ and a standard Gaussian $\nu$. Applied to model activations instead of audio, it looks for directions where the data spikes and clusters rather than the smooth spread PCA optimizes for.
Why non-Gaussianity happens to track interpretability here
The paper's own explanation for ICA's relative strength ties directly to Interpretability-vs-kurtosis/skew correlation analysis: interpretability score correlates with a feature's skew and kurtosis, and "this also explains why Independent Component Analysis (ICA), which maximises the non-Gaussianity of the found components, is the best performing of the alternatives that we considered" (sparse-autoencoders, §"C.4 INTERPRETABILITY SCORES CORRELATE WITH KURTOSIS AND SKEW OF ACTIVATION", p. 16). The advantage is not stable across the whole network, though: the sparse dictionary's lead over baselines "declines as we move through the model, being comparable to ICA in layer 4 and showing minimal improvement in the final layer" (sparse-autoencoders, §"3.2 SPARSE DICTIONARY FEATURES ARE MORE INTERPRETABLE THAN BASELINES", p. 5). And the comparison is not run on equal footing to begin with: ICA is fit on only about 2GB of data -- roughly 4 million residual-stream activations, versus the 5-50M vectors used to train the autoencoders and estimate PCA online -- because ICA algorithms converge far more slowly at scale (sparse-autoencoders, §"3.2 SPARSE DICTIONARY FEATURES ARE MORE INTERPRETABLE THAN BASELINES", p. 3), so its closing of the gap in later layers happens despite a smaller training budget, not because of a larger one.