Concepts Whisper While Syntax Shouts: Spectral Anti-Concentration and the Dual Geometry of Transformer Representations

A transformer's answer lives on one axis: the direction its unembedding reads. Its intermediate states largely do not, and that off-axis position is usually treated as an obstacle to interpretation. We show it is functional. A 12-layer model computes in two phases. Through the first, every sublayer writes into a subspace held near-orthogonal to the read-out, attention 75 to 96 degrees off it at every depth. Moving attention's values onto the read-out is 64 to 84 times more damaging than a matched random rotation, and the damage is entirely in cross-token mixing: the subspace insulates composition from the vocabulary. Beneath it the frame itself turns rigidly with depth. In the second phase the answer arrives on-axis, late, and by addition rather than by turning accumulated content onto the read-out. Pressing every layer onto the read-out instead, as training for early exit does, matches the baseline on perplexity, LAMBADA and BLiMP while cutting the concept-phase workspace from about twenty-five effective dimensions to fourteen, a change none of those benchmarks register. The geometry can also be imposed, though not by asking for it. Prescribing it through the loss is a lottery: six of eight seeds collapse, because a model told to null its read-out projection obeys most cheaply by discarding dimensions. Inserting one fixed rotation at the phase boundary lands it instead, at baseline quality. A sparse rotation the surrounding weights can absorb converges on all nine seeds, against five of nine for ordinary training. Which rotation is immaterial: twenty-five runs across thirteen distinct ones reach the same quality, and two baselines from different seeds hold their concepts in near-orthogonal frames while agreeing on their read-outs. That freedom is usable: a basis drawn at random and prescribed before training is adopted across the concept phase, with quality unchanged.

Concept formation in transformer language models is depth-extended, not a single-layer event: concepts emerge gradually across a contiguous region of the residual stream. Mechanistic interpretability methods identify the single layer of peak class separation -- the "best layer" -- capturing a snapshot rather than the process itself. We introduce the Concept Allocation Zone (CAZ): the depth interval within which a concept becomes measurably separable, the region allocated to its geometric expression. We formalize the CAZ through three layer-wise metrics (Separation, Concept Coherence, Concept Velocity) and derive principled boundary detection without manual layer sweeps. A CAZ is not a concept: it is the depth region within which the model organizes its geometry to make a concept separable. A single concept typically participates in multiple CAZes; multiple concepts may share one. Empirical validation across 34 models from 8 architectural families and 7 concepts reveals that the separation curve S(l) is frequently multimodal. A scored detector uncovers "gentle CAZes" -- subtle allocation regions invisible to standard peak detection but causally active in 93-100% of cases under ablation (16 of 34 models; 26 in the companion validation paper). The framework generates seven testable predictions; four yield clear verdicts (two not supported, one partially supported, one supported), one had its precondition invalidated by the data, and two are underpowered -- with cross-architecture alignment confirmed as depth-matched rather than monolithic under leave-one-concept-out cross-validation. Reference implementation: rosetta_tools v1.3.1 (doi:10.5281/zenodo.20361433).

The quadratic scaling of Transformer self-attention has driven the adoption of sub-quadratic Selective State Space Models (SSMs) like Mamba, which compress past context into a fixed-size recurrent hidden state. This strict informational bottleneck raises a foundational question for mechanistic interpretability: do SSMs and Transformers learn fundamentally distinct latent representations? In this work, we employ Sparse Autoencoders (SAEs) to conduct a large-scale, feature-level correspondence analysis between Mamba-130m and Pythia-70m over a 10-million token corpus. Contrary to hypotheses predicting widespread architectural divergence, we find no evidence of systematic representational divergence between architectures: across the observed Jaccard distribution, 99.98% of Mamba features cluster toward the upper alignment boundary, providing preliminary feature-level support for the Universality Hypothesis. We further identify and qualitatively characterize this microscopic fraction (0.02%) of diverging features, finding patterns consistent with the hypothesis that the recurrent bottleneck selectively limits the parsing of rigid syntax rather than broad semantic ontology. We demonstrate that while Pythia's unconstrained attention permits the monosemantic decomposition of distinct formatting edge-cases, Mamba is forced to compress unrelated syntactical anomalies into polysemantic "junk drawer" neurons to preserve state capacity. Collectively, these results suggest that architectural routing mechanisms may have negligible impact on core semantic understanding, with representational divergence confined to extreme structural margins.