In-context belief updating traces a low-dimensional manifold

Bigelow et al. measure Llama-3.1-8B-Instruct's belief about story concepts (emotions, genres, an arbitrary control) as an expected value over next-token digit probabilities, tracing a smooth trajectory through a UMAP/PCA-recovered low-dimensional manifold [bigelow-etal-2026] The same low-dimensional structure is recoverable from residual-stream activations, correlating with the behavioral geometry (r=.92) for structured domains but not the arbitrary control [bigelow-etal-2026] For emotions the manifold reduces to a 2D valence-arousal plane matching Russell's circumplex, a flat linearly-probeable subspace [bigelow-etal-2026] Activation-addition steering along a concept direction predictably shifts belief, and unintended steering entanglement is predictable from geometric distance between concepts [bigelow-etal-2026] The model-id and diff-in-means extraction were not confirmable from the available render, so those details are deferred, though the geometric findings hold [bigelow-etal-2026]