Linear representations of sentiment — cross validates against pca for → Mean Difference (MD) vector extraction

Before CAA existed, Tigges et al. (2023) had already shown that Mean Difference vectors for sentiment closely resemble the directions PCA finds — the same fact CAA cites when introducing MD: "this method of extracting the difference vector is called Mean Difference (MD) and has been shown to produce steering vectors similar to other techniques like PCA (Tigges et al., 2023)" (contrastive-activation-addition, §"3 Method", p. 3). The significance of that citation is what it rules out: MD is a supervised procedure — it needs labeled positive and negative examples and simply averages their difference — while PCA is unsupervised, finding whatever direction accounts for the most variance in an unlabeled activation cloud with no access to which examples exhibit the behavior. Two independent procedures with different information requirements converging on the same direction for sentiment is evidence that the direction reflects something real about how the model represents the concept, rather than an artifact of MD's particular averaging procedure. That prior, sentiment-specific validation is part of why CAA can adopt bare Mean Difference for seven different behaviors without first re-deriving or re-justifying the extraction method itself.