  The task of out-of-distribution (OOD) detection is crucial for deploying
machine learning models in real-world settings. In this paper, we observe that
the singular value distributions of the in-distribution (ID) and OOD features
are quite different: the OOD feature matrix tends to have a larger dominant
singular value than the ID feature, and the class predictions of OOD samples
are largely determined by it. This observation motivates us to propose
\texttt{RankFeat}, a simple yet effective \emph{post hoc} approach for OOD
detection by removing the rank-1 matrix composed of the largest singular value
and the associated singular vectors from the high-level feature.
\texttt{RankFeat} achieves \emph{state-of-the-art} performance and reduces the
average false positive rate (FPR95) by 17.90\% compared with the previous best
method. The success of \texttt{RankFeat} motivates us to investigate whether a
similar phenomenon would exist in the parameter matrices of neural networks. We
thus propose \texttt{RankWeight} which removes the rank-1 weight from the
parameter matrices of a single deep layer. Our \texttt{RankWeight}is also
\emph{post hoc} and only requires computing the rank-1 matrix once. As a
standalone approach, \texttt{RankWeight} has very competitive performance
against other methods across various backbones. Moreover, \texttt{RankWeight}
enjoys flexible compatibility with a wide range of OOD detection methods. The
combination of \texttt{RankWeight} and \texttt{RankFeat} refreshes the new
\emph{state-of-the-art} performance, achieving the FPR95 as low as 16.13\% on
the ImageNet-1k benchmark. Extensive ablation studies and comprehensive
theoretical analyses are presented to support the empirical results.
