The Limits of Replacing Attention Heads: Capacity and Robustness in Static Retrieval

Can query slots replace attention heads without sacrificing retrieval capacity or reliability? To the best of our knowledge, we establish the first joint sharp characterization of these two resources for static quadratic-coverage retrieval. For one tokenwise pooling round with $h$ heads, $R$ fixed query slots per head and $K=hR$ reads, stable length-uniform approximation of coverage over $D$ prototypes is possible exactly when $K\ge D$. The converse allows arbitrary finite value width, length-dependent scores and joint nonlinear Lipschitz decoding, without a data-dependent bypass. Reliability obeys a different law: against $s$ hidden whole-head corruptions, uniformly beating the constant baseline over unbounded count imbalance with bounded decoder–value sensitivity requires $h\ge 2s+1$ and $hR\ge (2s+1)D$, with matching constructions under sufficient contrast and noise margin. Exact finite-budget minimax frontiers quantify what read allocation, score contrast, value scale, noise and decoder sensitivity can and cannot compensate for. An exact decoder oracle isolates fixed-source representation limits, while a count-uniform certificate supplies trainable robust margins over an infinite known-prototype multiset class. All 20 construction-matched fits attain the predicted finite-budget frontiers, and 2,592 grouped-fault configurations match the exact formula. After a 100-step teacher prefix, direct-margin continuation recovers certified robustness in 15/15 fresh blocks at $D=8,16,32$. Complementary frozen-Qwen3-4B stress tests probe bounded readout and native-head sensitivity, not transfer of the static theorem. The result separates interchangeable read channels from irreplaceable fault domains.