The Communication Map of a Transformer

Mechanistic interpretability has identified transformer circuits, but lacks a shared vocabulary for describing how their functions compose across tasks and architectures. We introduce Coherentist Probabilistic Compositionalism (CPC), an interpretive framework that grounds transformer computation in coherentist theories of interpretation and describes it through four operator roles. Alignment identifies candidate relations, unification integrates supporting information, suppression reduces incompatible alternatives, and routing carries selected information to the output. Across 15 models from five architecture families, the suppression, unification, and routing weight-space signatures correlate with held-out activation-level role measures above random baselines. Suppression is more stable across tasks than unification. Ablating alignment heads reduces downstream suppressive activity beyond a random-head control in 10 models, but similar effects on no-conflict prompts indicate a general upstream dependency, not contradiction-specific coupling. Explicit contradictions significantly shift a layerwise coherence proxy in 14 models; after removing shared residual covariance, the gap has the predicted direction in every model. Base and instruction-tuned variants preserve induction-head score structure ($r{\geq}0.98$) without a consistent shift of operator signatures towards later layers. These results support CPC as a shared vocabulary for comparing transformer mechanisms while showing that their depth and geometric expression remain architecture-specific.

A transformer MLP gives each hidden channel two roles: a reader that decides when the channel responds, and a writer that decides what it adds back to the residual stream. Read as a key--value memory, the layer can be measured one factor set at a time: the pairing of readers to writers is carried only by their shared index, invisible to any quantity computed from one factor set alone. Yet training couples the two factors through their joint update, so we ask what reading them together shows. The block supplies the joint instrument: the MLP writes back into the very stream it reads, so the exact Jacobian of its update is square, and its agreement with its own transpose resolves into reader--writer terms whose inner products give each channel, read as a couple, a signed pairing coordinate. Ranked by this coordinate, each block we measure has a small core of strongly coupled channels; where initialization gives either sign equally, the core is nearly all opposed: each writer points against the direction its reader responds to. This opposed core recurs from the smallest models trained from scratch to released checkpoints; its sign is in place within a few percent of training and holds while the coupling grows. Read as couples, most channels return their contribution against the reader that fired it, and the readers of later blocks take it up; few show in the logits. Training holds the couples in place: flipping the opposed writers moves the output toward common tokens, and a writer permuted onto another reader regrows to fit that reader while the reader stays.

Transformer language models build predictions through successive residual updates, but how their representations become specific to an eventual outcome remains unclear. We study this process by comparing intermediate residual states with their own final states and an empirical bank of final states from other contexts. Across six pretrained language models, the own endpoint becomes preferable to the average alternative early, while many individual endpoints remain closer. These competing sets generally shrink with depth, but their membership changes and their surviving endpoints need not become more similar to one another. Directional alignment and endpoint rank can therefore improve while Euclidean distance to the final state changes little. We develop a simple high-dimensional model that separates the roles of norm, alignment, and endpoint geometry, showing how gradual directional changes can produce sharp reductions in competition. We also prove that a straight path toward the own endpoint cannot introduce new competitors under either Euclidean or cosine distance; observed entries thus establish departures from straight-line convergence. Finally, endpoints associated with lower-ranked output tokens tend to lie farther away in cosine distance across all studied models, connecting residual geometry to output organization. Together, these findings characterize increasing geometric specificity during transformer inference and explain why distance, competitor count, and concentration of the surviving endpoints provide distinct views of that process.