Principal Component Analysis (PCA) — is the projection technique behind → PCA visualization of contrastive activations

PCA is the off-the-shelf machinery underneath activation-pca-visualization: the technique itself is inherited from decades of dimensionality-reduction work and applied directly via the Scikit-learn package rather than reimplemented for this paper (contrastive-activation-addition, §"3.2 Visualizing activations for contrastive dataset analysis", p. 4). What CAA contributes is not a new projection method but a specific use of an old one -- projecting high-dimensional residual-stream activations from a contrastive dataset down to their top two principal components, the axes of greatest variance, and checking by eye whether the resulting scatter separates by behavior. Two components turn out to be enough: the paper's figures show refusal-behavior clustering becoming visible in a plain two-dimensional plot at layer 10, with no need for higher-dimensional projections or a trained classifier to detect the split. That a linear, unsupervised, general-purpose technique is sufficient to reveal the separation is itself part of the paper's evidence that these behavioral representations are simple, linear directions rather than more complex, entangled features.