Independent Component Analysis (ICA)

Assumptions and requirements

In ICA, each column in $W \in \mathbb{R}^{d \times m}$ is a mixing vector, and m is the number of different source signals; each row in $S \in \mathbb{R}^{m \times n}$ is a source signal (a signal has n data points), with m source signals in total. These signals are optimised to be independent of one another. Thus, if model activations are linear mixtures of statistically independent “foundational features”, ICA can provably recover those features.

Evaluation considerations

More recently, however, Liu & Han (2026) showed that ICA can achieve performance comparable to that of SAEs, arguing that its previously reported underperformance may stem from limitations of classical ICA implementations poorly suited to the scale and statistical structure of neural network activations.

Limitations

Moreover, underlying features may not be statistically independent, which further limits the applicability of classical ICA. Although early studies applied it to analyse neural network activations, they did not find interpretability gains over SAEs (Cunningham et al., 2024).

Related methods

• Sparse Autoencoders (SAEs)

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Key papers

Cited in §6.9.3.

• ■ Aapo Hyvärinen and Erkki Oja. Independent component analysis: algorithms and applications. Neural networks, 13 (4-5): 411–430, 2000.
• ■ Michael S. Lewicki and Terrence J. Sejnowski. Learning overcomplete representations. Neural Comput., 12 (2): 337–365, February 2000. ISSN 0899-7667. . URL https://doi.org/10.1162/089976600300015826.
• ■ Hoagy Cunningham, Aidan Ewart, Logan Riggs, Robert Huben, and Lee Sharkey. Sparse autoencoders find highly interpretable features in language models. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=F76bwRSLeK.
• ■ PreprintSida Liu and Feijiang Han. Ica lens: Interpreting language models without training another dictionary, 2026. URL https://arxiv.org/abs/2606.11722.

Other methods in Comparison with Alternative Feature Extraction Methods

Non-Negative Matrix Factorisation (NMF) · Principal Component Analysis (PCA) · Supervised Feature Extraction Methods (DAS, SMDS, probes) · Dictionary Learning Baselines (K-SVD)