analiza aiqbench
This research provides a rigorous mathematical analysis of parameter identifiability within deep normalized attention mechanisms, specifically proving the real-analytic case of a longstanding conjecture regarding softmax and other normalizers. By characterizing conditions under which later attention scores become unobservable due to query/key collapse, the work offers critical insights into the numerical sensitivity and structural limits of transformer architectures.
The Identifiability and Observability of Deep Normalized Attention
arXiv:2610.09620v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2610.09620 [cs.LG]
(or arXiv:2610.09620v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.09620 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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