Concept Subspaces Compute Beyond the Logit Lens: A Weights-Only Test for Locating Representations Upstream of Readout
On the map: Mechanistic interpretability → Steering and interpreting LLM reasoning
Abstract (arXiv)
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 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. A complementary four-model, three-seed intervention study finds model-dependent source-directed effects that remain well below full-vector replacement. Together, the geometry and intervention controls distinguish concept structure from dominant readout directions while limiting claims of causal sufficiency.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Steering and interpreting LLM reasoning, one of 13 directions in Mechanistic interpretability. Builds on 8 of its 45 references that are in the map. First posted on arXiv 30 Sep 2026.
Builds on
8 of 45 references.
Closest ancestors · 1
Same direction, newest first
- 2026Hidden Error Awareness in Chain-of-Thought Reasoning: The Signal Is Diagnostic, Not Causal10 May
Other references · 7
- 2021Training Verifiers to Solve Math Word Problemscited by 10,109
- 2023Universal and Transferable Adversarial Attacks on Aligned Language Modelscited by 3,104
- 2023Steering Language Models With Activation Engineeringcited by 922
- 2023Eliciting Latent Predictions from Transformers with the Tuned Lenscited by 623
- 2025Prototype-Based Dynamic Steering for Large Language Modelscited by 6
- 2026Steerable but Not Decodable: Function Vectors Operate Beyond the Logit Lenscited by 6
- 2026Predicting Where Steering Vectors Succeedcited by 4
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2026Beyond Language: Format-Agnostic Reasoning Subspaces in Large Language Models
- 2023Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching
- 2026The Master Key Hypothesis: Unlocking Cross-Model Capability Transfer via Linear Subspace Alignment
- 2025Toward a Flexible Framework for Linear Representation Hypothesis Using Maximum Likelihood Estimation
- 2026Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States
- 2026The Gradient Does Not See Rank: Rank-Indifference in Matrix-CODI on ProsQA
- 2026Lingtai: What Concept Geometry Reveals--and Does Not Reveal--About LLM Inference
- 2026H-Probes: Extracting Hierarchical Structures From Latent Representations of Language Models