We introduce SNAP (Self-coNsistent Agreement Principle), a self-supervised framework for robust computation based on mutual agreement. Based on an Agreement-Reliability Hypothesis SNAP assigns weights that quantify agreement, emphasizing trustworthy items and downweighting outliers without supervision or prior knowledge. A key result is the Exponential Suppression of Outlier Weights, ensuring that outliers contribute negligibly to computations, even in high-dimensional settings. We study properties of SNAP weighting scheme and show its practical benefits on vector averaging and subspace estimation. Particularly, we demonstrate that non-iterative SNAP outperforms the iterative Weiszfeld algorithm and two variants of multivariate median of means. SNAP thus provides a flexible, easy-to-use, broadly applicable approach to robust computation.

翻译：本文提出SNAP（自洽一致性原则），一种基于相互一致性的自监督鲁棒计算框架。基于一致性-可靠性假设，SNAP通过分配量化一致性的权重，在无需监督或先验知识的情况下强调可信数据项并降低异常值权重。核心成果是异常值权重的指数抑制特性，确保即使在高维场景下异常值对计算的贡献可忽略不计。我们研究了SNAP加权方案的性质，并展示了其在向量平均和子空间估计中的实际优势。特别地，我们证明非迭代的SNAP方法优于迭代的Weiszfeld算法以及两种多元均值中位数变体。因此，SNAP为鲁棒计算提供了一种灵活、易用且广泛适用的方法。