Color representations trace a paraboloid (circular hue and lightness)

measured in 1 paper

Bhalla et al. show color representations in Llama-3.1-8B (layer 19, hex-code prompts) organize along a paraboloid with a circular hue dimension and a lightness dimension, rather than a flat cylinder [bhalla-etal-2026] Fitting PCA and steering the activation along interpolated points between hue-bin centroids produces smooth, predictable shifts in the predicted color-name tokens, so the geometry is causally load-bearing [bhalla-etal-2026] A cross-lingual companion in NLLB-200 recovers the same hue-circle-plus-lightness-axis shape, though as a flat orthogonal decomposition rather than a fused paraboloid and without a causal test [bhalla-etal-2026]

Structure

Paraboloid (circular × pinched continuum)

Context

color, hue, manifold ubiquity

Confirmed in models

Llama-3.1-8B · Llama

Method

PCA, Activation Steering (Addition)

Papers

Do Sparse Autoencoders Capture Concept Manifolds? — Bhalla, Usha, Fel, Thomas, Rager, Can, Feucht, Sheridan, Haklay, Tal, Wurgaft, Daniel, Boppana, Siddharth, Kowal, Matthew, Shyam, Vasudev, Lewis, Owen, McGrath, Thomas, Merullo, Jack, Geiger, Atticus, Lubana, Ekdeep Singh2026 · arXiv:2604.28119