Capacity without Access: Reinterpreting the Mid-Depth Spectral Plateau in LLMs

Prior probing-based analyses show that individual layers specialize in distinct linguistic and semantic functions, while a complementary line of work observes that deeper layers enter an alignment-dominated regime where residual transformations become increasingly constrained relative to the evolving hidden-state geometry. These findings appear to conflict: layer-wise functional specialization versus apparent representational stagnation in deeper layers. This raises a key question: Is the observed representational stagnation in deeper layers attributable to suboptimal acquisition or encoding of novel features, or are these features learned appropriately but exhibit minimal marginal contribution to the model’s predictive output? We address this by separating model behavior into (i) representational capacity: the richness and spectral diversity of the encoded features, and (ii) accessibility: the extent to which these features are aligned with, and exploited by, the output-relevant subspace. Analyzing hidden-state second-moment geometry across depth shows that intermediate layers maintain a broad representational span and rich spectral diversity, yet project only weakly onto the output-relevant subspace, indicating intact representational capacity but constrained accessibility within task-relevant dimensions. To probe their functional relevance, we add a controlled diagnostic pathway that routes intermediate-layer embeddings to the terminal readout. Analysis of the induced behavioral changes indicates that the apparent stagnation is better accounted for by geometric limitations on accessibility, rather than by a deficit in representational capacity. The source code is available here.