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This paper formalizes memory poisoning attacks on retrieval-augmented LLM agents as a Stackelberg game and introduces MEMSAD, a gradient-coupled anomaly detection defense. MEMSAD leverages a theoretical result showing that under encoder regularity, anomaly score gradients and retrieval objective gradients are provably identical, enabling a certified detection radius. Experiments demonstrate that MEMSAD, when combined with other defenses, achieves perfect TPR and FPR, but is vulnerable to synonym substitution attacks, highlighting limitations of continuous-space defenses.
Retrieval-augmented LLMs are surprisingly vulnerable to memory poisoning via synonym substitution, a loophole that gradient-based defenses can't close.
Persistent external memory enables LLM agents to maintain context across sessions, yet its security properties remain formally uncharacterized. We formalize memory poisoning attacks on retrieval-augmented agents as a Stackelberg game with a unified evaluation framework spanning three attack classes with escalating access assumptions. Correcting an evaluation protocol inconsistency in the triggered-query specification of Chen et al. (2024), we show faithful evaluation increases measured attack success by $4\times$ (ASR-R: $0.25 \to 1.00$). Our primary contribution is MEMSAD (Semantic Anomaly Detection), a calibration-based defense grounded in a gradient coupling theorem: under encoder regularity, the anomaly score gradient and the retrieval objective gradient are provably identical, so any continuous perturbation that reduces detection risk necessarily degrades retrieval rank. This coupling yields a certified detection radius guaranteeing correct classification regardless of adversary strategy. We prove minimax optimality via Le Cam's method, showing any threshold detector requires $\Omega(1/\rho^2)$ calibration samples and MEMSAD achieves this up to $\log(1/\delta)$ factors. We further derive online regret bounds for rolling calibration at rate $O(\sigma^{2/3}\Delta^{1/3})$, and formally characterize a discrete synonym-invariance loophole that marks the boundary of what continuous-space defenses can guarantee. Experiments on a $3 \times 5$ attack-defense matrix with bootstrap confidence intervals, Bonferroni-corrected hypothesis tests, and Clopper-Pearson validation ($n=1{,}000$) confirm: composite defenses achieve TPR $= 1.00$, FPR $= 0.00$ across all attacks, while synonym substitution evades detection at $\Delta$ ASR-R $\approx 0$, exposing a gap existing embedding-based defenses cannot close.
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