The Identifiability and Observability of Deep Normalized Attention

Abstract

We study which parameters of deep, unmasked, single-head attention are determined by its input--output function. For known positive nonconstant real-analytic normalizers, the function generically determines the effective scores and combined value map up to the signs induced by even normalizers. This proves the real-analytic case of a conjecture of Henry--Marchetti--Kohn, including softmax. We then classify exceptional fibers under explicit normalizer conditions, identifying when collapse makes later scores unobservable, and establish sharp Taylor orders for local identification. Near simultaneous query/key collapse, we compute the complete native Jacobian decay spectrum on separating finite input banks. For common first nonconstant normalizer degree $k$, layer $i$ has contact order $2k3^{i-1}-1$, with exact multiplicities and kernel dimension. High-precision and automatic differentiation calculations illustrate the resulting loss of numerical sensitivity.