The article introduces Semantic Reference Frames (SemRF), an anchor-based formalism designed to separate semantic measurement from residual dynamics in language models. This approach fixes anchors to measure states against them, addressing the issue where intermediate decoding requires comparable readout coordinates across layers.
- SemRF uses pseudo-inverse tying for exact synchronization and yields stable semantic-basis coordinates under restricted bi-invertibility.
- The method induces a semantic Voronoi diagram that assigns each layer to a coarse cell based on distance or logits while retaining within-cell motion.
- It defines layerwise steps, contribution profiles, and imbalance diagnostics to trace residual computation as a depthwise semantic trajectory.
- The canonical trace is defined as the minimum-action path inside a margin-relaxed tube, obeying a discrete spline equation when nonempty.
- Low curvature in these traces implies piecewise-linear compressibility and local knowledge density, linking lower trace complexity to fewer semantic degrees of freedom.
The authors argue that this framework provides a conditional link between parameter efficiency and trajectory complexity, allowing for the analysis of residual computation through controlled interface error and projection residual constraints.