Detecting out-of-distribution (OOD) samples is essential for ensuring the
reliability of deep neural networks (DNNs) in real-world scenarios. While
previous research has predominantly investigated the disparity between
in-distribution (ID) and OOD data through forward information analysis, the
discrepancy in parameter gradients during the backward process of DNNs has
received insufficient attention. Existing studies on gradient disparities
mainly focus on the utilization of gradient norms, neglecting the wealth of
information embedded in gradient directions. To bridge this gap, in this paper,
we conduct a comprehensive investigation into leveraging the entirety of
gradient information for OOD detection. The primary challenge arises from the
high dimensionality of gradients due to the large number of network parameters.
To solve this problem, we propose performing linear dimension reduction on the
gradient using a designated subspace that comprises principal components. This
innovative technique enables us to obtain a low-dimensional representation of
the gradient with minimal information loss. Subsequently, by integrating the
reduced gradient with various existing detection score functions, our approach
demonstrates superior performance across a wide range of detection tasks. For
instance, on the ImageNet benchmark, our method achieves an average reduction
of 11.15% in the false positive rate at 95% recall (FPR95) compared to the
current state-of-the-art approach. The code would be released.

通过对梯度信息进行线性降维，结合现有的检测评分函数，我们的方法在各种检测任务中展示了卓越的性能，例如在 ImageNet 基准测试中，我们的方法相较于当前最先进方法，在 95% 召回率时，假阳性率平均减少了 11.15%。

低维度梯度有助于外部分布检测

Low-Dimensional Gradient Helps Out-of-Distribution Detection

We perform a non-asymptotic analysis on the singular vector distribution
under Gaussian noise. In particular, we provide sufficient conditions on a
matrix for its first few singular vectors to have near normal distribution. Our
result can be used to facilitate the error analysis in linear dimension
reduction.

本文对高斯噪声下的奇异向量分布进行了非渐近分析，特别地，我们给出了一个矩阵的充分条件，使其前几个奇异向量具有近似正态分布。我们的结果可用于线性降维中的误差分析。