When Does Content-Based Routing Work? Representation Requirements for Selective Attention in Hybrid Sequence Models

We identify a routing paradox in hybrid recurrent-attention architectures: content-based routing - deciding which tokens deserve expensive attention - requires exactly the pairwise computation that routing is designed to avoid. Through 20+ controlled experiments across three tasks (a synthetic diagnostic, the Zoology MQAR benchmark, and HotpotQA), we map the routing landscape exhaustively. One layer of softmax attention creates a latent ~34-dimensional subspace enabling 98.4% routing precision; zero layers yield 1.2%. This subspace is invisible to cosine similarity, destroyed by random projections (98.4% to 2.6%), and cannot be created by contrastive pretraining - proving attention's role is writing pairwise match results into representations, not merely computing them. Twelve alternative mechanisms all cluster at 15-29%. Non-learned indices (Bloom filter: 90.9%; BM25 on HotpotQA: 82.7%) bypass the bottleneck entirely. The result is a sharp two-regime hierarchy with an empty middle ground. These findings provide the mechanistic explanation for the empirical observation that recurrent models fail at associative recall, and reframe attention as a representation constructor rather than merely a computation mechanism.