Relational Linear Properties in Language Models: An Empirical Investigation

We study how large language models recall relational knowledge during text generation, with a focus on identifying latent representations suitable for relation classification via linear probes. Prior work shows how attention heads and MLPs interact to resolve subject, predicate, and object, but it remains unclear which representations support faithful linear relation classification and why some relation types are easier to capture linearly than others. We systematically evaluate different latent representations derived from attention head and MLP contributions, showing that per-head attention contributions to the residual stream are comparatively strong features for linear relation classification. Feature attribution analyses of the trained probes, as well as characteristics of the different relation types, reveal clear correlations between probe accuracy and relation specificity, entity connectedness, and how distributed the signal on which the probe relies is across attention heads. Finally, we show how token-level feature attribution of probe predictions can be used to reveal probe behavior in further detail.

Linear probing of large language model (LLM) hidden states is widely used to claim that models learn distinct representations for different reasoning types. We test this by probing Qwen3-14B on three benchmarks spanning the classical trichotomy: LogiQA 2.0 (deductive), ARC-Challenge (inductive), and $α$NLI (abductive). At layer 32 of 40, linear probes achieve 100% cross-validated accuracy with well-separated geometry (intrinsic dimensionalities: 20.6, 28.5, 33.6; convex hull contamination $\leq$1.5%). However, this separation is entirely driven by format confounds. Residualizing source identity, option count, and response length reduces accuracy to chance. Trace-anchor similarity indicates largely shared reasoning across tasks (42.5% agreement vs.\ 33.3% chance), and causal steering with random controls ($n=20$) shows no functional link between geometry and reasoning mode ($p=0.286$). Thus, high probe accuracy reflects task format rather than computational structure, motivating routine format deconfounding in mechanistic interpretability.

The Linear Representation Hypothesis associates high-level concepts with directions in language models, but it remains unclear how these concept-related linear structures are organized within the model. We propose the Answer-Basin Representation Hypothesis: the probability measure induced over answers by the model's continuation distribution organizes these linear structures, with its statistics represented along linear directions shared across questions. All continuations yielding the same answer form an answer basin, whose mass is their total probability. These basin masses define the pushforward probability measure over answers. We posit that concept-related linear structure emerges from differences in the answer measure rather than being determined by changes in concept labels. Experiments across models and tasks link concept-consistent effects and their reversals in probing and steering to the alignment between concept labels and the answer measure.