Open-ended scalar concepts trace affine 1D lines

Bhalla et al. find simple open-ended scalar concepts (temperature, age) trace flat open 1D lines in Llama-3.1-8B's layer-19 residual stream, via PCA across sampled prompt values [bhalla-etal-2026] Causal steering along interpolated points between binned centroids is validated only for temperature, color, and day-of-week (e.g. freezing to cold to warm to hot), producing smooth monotonic output shifts [bhalla-etal-2026] Age and years show the same open 1D structure by PCA but were not steered, so their causal load-bearing status is not established here [bhalla-etal-2026] Formality, sentence length, and a synthetic political-bias score show similar roughly-1D structure with PCA evidence only [bhalla-etal-2026]