PAEC $k$NN-MT: Stabilizing Retrieval-Augmented Translation via Lyapunov-Guided Control

ACL ARR 2026 January Submission2448 Authors

Keywords: kNN-MT, retrieval-augmented translation, Lyapunov stability, Control Lyapunov Function, exposure bias, dynamical systems, neural machine translation, policy distillation

Abstract: $k$-Nearest Neighbor Machine Translation ($k$NN-MT) enables effective domain adaptation but suffers from greedy per-step decisions that ignore long-term consequences, amplifying \emph{exposure bias} as early errors compound throughout translation. We propose PAEC (Production-Aware Exposure Control), which reframes $k$NN-MT retrieval control as a dynamical system stabilization problem. PAEC models decoding as an $11$-dimensional state evolution and learns a Transformer-based dynamics model $\mathcal{T}_\theta$ with provable \emph{Lipschitz continuity}. By enforcing \emph{Control Lyapunov Function} conditions, we derive policies guaranteeing \emph{Ultimate Uniform Boundedness}: errors converge to a bounded neighborhood with high probability. On De-En translation under constrained settings (enforced retrieval, limited datastore), PAEC reduces the failure rate from $34.2$% to $29.3$% $\left(p < 10^{-12}\right)$. While Adaptive $k$NN-MT degenerates to Pure NMT $\left(\lambda \to 0\right)$, PAEC stabilizes the retrieval pathway, demonstrating tail-risk avoidance. Finally, we distill the online controller into an offline policy, achieving $93$% latency reduction while preserving comparable stability guarantees. As a control layer orthogonal to retrieval mechanisms, PAEC enables integration with other $k$NN-MT variants.

Paper Type: Long

Research Area: Machine Translation

Research Area Keywords: domain adaptation,efficient inference for MT,modeling,retrieval-augmented generation,optimization methods

Contribution Types: Model analysis & interpretability, NLP engineering experiment, Theory

Languages Studied: German, English

Submission Number: 2448