[2604.01683] Coupled Query-Key Dynamics for Attention

Computer Science > Machine Learning arXiv:2604.01683 (cs) [Submitted on 2 Apr 2026] Title:Coupled Query-Key Dynamics for Attention Authors:Barak Gahtan, Alex M. Bronstein View a PDF of the paper titled Coupled Query-Key Dynamics for Attention, by Barak Gahtan and 1 other authors View PDF HTML (experimental) Abstract:Standard scaled dot-product attention computes scores from static, independent projections of the input. We show that evolving queries and keys \emph{jointly} through shared learned dynamics before scoring - which we call \textbf{coupled QK dynamics} - improves language modeling perplexity and training stability. On WikiText-103 at 60M parameters, coupled dynamics achieves 22.55--22.62 perplexity vs.\ 24.22 for standard attention ($-$6.6--6.9\%), with only 0.11\% additional parameters (shared across both instantiations). A structural ablation isolates coupling as the active ingredient: a symplectic (Hamiltonian) and a non-symplectic (Euler) integrator perform identically when both couple Q and K, while an uncoupled MLP baseline of matched capacity reaches only 23.81 with 8$\times$ higher seed variance. The integration step count (1--7) is similarly irrelevant - a single coupled step suffices. A compute-matched comparison reveals that coupling is a \emph{sample-efficiency} mechanism: standard attention trained for 2.4$\times$ longer (matching wall-clock) reaches the same perplexity, but requires 2.4$\times$ more tokens. The advantage scales to 150M ($-$6.7\%) bu...