We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP algorithm $\mathcal A$, our algorithm performs a spectral pre-processing step and then mildly modifies the iterates of $\mathcal A$. If given the perturbed input $X + E \in \mathbb R^{n \times n}$ for any $E$ supported on a $\varepsilon n \times \varepsilon n$ principal minor, our algorithm outputs a solution $\hat v$ which is guaranteed to be close to the output of $\mathcal A$ on the uncorrupted $X$, with $\|\mathcal A(X) - \hat v\|_2 \le f(\varepsilon) \|\mathcal A(X)\|_2$ where $f(\varepsilon) \to 0$ as $\varepsilon \to 0$ depending only on $\varepsilon$.

翻译：我们提出了一种快速、基于谱的鲁棒近似消息传递（AMP）算法实现方法。对于任意具有独立亚高斯项的对称矩阵$X$上的二次优化问题，以及任意可分离的AMP算法$\mathcal A$，我们的算法首先执行谱预处理步骤，然后对$\mathcal A$的迭代进行温和修改。若给定扰动输入$X + E \in \mathbb R^{n \times n}$（其中$E$支撑在$\varepsilon n \times \varepsilon n$的主子矩阵上），算法可保证输出解$\hat v$接近$\mathcal A$在未受污染数据$X$上的输出，满足$\|\mathcal A(X) - \hat v\|_2 \le f(\varepsilon) \|\mathcal A(X)\|_2$，且$f(\varepsilon) \to 0$当$\varepsilon \to 0$，该函数仅依赖于$\varepsilon$。