Concept Subspaces Compute Beyond the Logit Lens: A Weights-Only Test for Locating Representations Upstream of Readout
A concept subspace's effect on model behavior does not establish how it relates to the output readout. We introduce a two-sided geometric diagnostic that measures an extracted subspace's overlap with the dominant right-singular directions of the unembedding matrix, evaluated against output-oriented positive controls. Given an extracted basis, the raw diagnostic requires only model weights. Our testbed is the Format-Agnostic Reasoning Subspace (FARS), a ten-dimensional basis extracted from eighteen reasoning concepts expressed in six surface forms. Across nine rank-matched estimators and twenty-six models, four activation-derived concept estimators carry only 0.38--0.80% mean energy in the...
| Authors | Aojie Yuan, Zhiyuan Julian Su, Haiyue Zhang et al. |
|---|---|
| Primary category | cs.CL |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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