Lexical Reference Frames: Interpreting LM Residual Streams in Native Semantics

Residual-stream analysis asks how language-model computation evolves across depth, but intermediate decoding requires comparable readout coordinates across layers. If embedding anchors and unembedding readout disagree on the chosen span, apparent motion may reflect measurement drift rather than computation. We introduce Semantic Reference Frames (SemRF), an anchor-based formalism separating semantic measurement from residual dynamics. A SemRF fixes anchors and measures states against them. Pseudo-inverse tying gives exact synchronization; under restricted bi-invertibility, SemRF yields stable semantic-basis coordinates, distortion bounds, and near-identity changes. With the frame fixed, residual computation becomes a depthwise semantic trajectory. The anchors induce a semantic Voronoi diagram: distance, or evidence such as logits, assigns each layer to a coarse cell, while coordinates retain within-cell motion and margins. We define layerwise steps, contribution profiles, and imbalance diagnostics, then use the Voronoi trace to define a margin-relaxed tube. The canonical trace is the minimum-action path inside this tube; when nonempty with positive quadratic weight, it is unique and obeys a discrete spline equation away from active constraints. Excess action controls step, curvature, and profile mismatch. Low curvature implies piecewise-linear compressibility and local knowledge density: lower trace complexity means fewer semantic knots. Through the parameter-to-trajectory map, this gives a conditional link to parameter efficiency: among admissible settings fitting data, lower-action and lower-complexity traces use fewer semantic degrees of freedom. The guarantees require controlled interface error and small projection residual under explicit tube constraints.

Representations extracted from large language models (LLMs) play an important role in many downstream applications. However, the structure of these representations is often influenced by lexical overlap rather than semantic content. Our understanding of the relationship between this lexical influence and semantic content, and its implications for downstream tasks, remains limited. In this work, we investigate representations to quantify the effect of lexical overlap relative to semantic content. We consider several adversarial semantic stress tests and further connect our findings to the information theory perspective. We find that lexical influence extends across the depth of models, consistently across architectures, training regimes, and objective functions, including the models trained for semantic similarity. Moreover, we observe a mid-depth region in which both lexical and semantic signals degrade simultaneously, indicating a transitional regime where representations are poor for both surface form and meaning. We further demonstrate the effect of lexical influence on downstream uses of LLMs using summarization and model editing as a case study.

Lexical representations can encode both abstract information and information specific to particular contexts. We investigate how these forms of information are organized in language models by decomposing contextual word representations into item, class, and word-class interaction components. Across six pretrained transformers and two linguistic categories, we find that the interaction is consistently present, grows across layers, and contains information associated with both item and class. Unlike the nearly orthogonal item and class effects, the interaction overlaps with both and encodes class information beyond the shared class effect. An interaction also emerges in artificial-language learners even when the input contains only additive structure. Together, these findings show that lexical representations combine abstract information with structure specific to particular word-class combinations.