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. 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 top-ten readout span. Final-layer PCA carries 3.56%, exceeding FARS in 25 of 26 models. A same-layer next-token control, evaluated using a fitted linear translator for depth matching, carries approximately thirteen times more energy than FARS, with separation in all 25 tested models. Re-extracting FARS on ten disjoint concepts yields 62–100% cross-format retrieval across twenty-four generative models, demonstrating transfer of the extraction procedure rather than a fixed basis. Analyses of three reasoning-tuned models further identify a distinct concept subspace in the sampled chain-of-thought tail. These findings distinguish concept structure from dominant linear readout directions under explicit controls. The diagnostic complements causal interventions; geometric separation alone does not establish the computation performed by a subspace.