While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.

翻译：尽管过参数化已知有利于泛化，但其对分布外检测的影响尚不明确。本文研究了模型复杂度在分布外检测中的作用。我们提出了一个期望分布外风险度量，用于评估分类器在训练样本和分布外样本上的置信度。借助随机矩阵理论，我们推导了应用于高斯数据的二元最小二乘分类器的期望分布外风险边界。我们证明，当参数数量等于样本数量时，分布外风险呈现无限峰值，我们将此与双下降现象相关联。我们在多种神经架构上对不同分布外检测方法进行的实验研究扩展了我们的理论洞见，并突显了双下降曲线。我们的观察表明，过参数化并不必然导致更好的分布外检测。利用神经坍缩框架，我们为更好地理解这一行为提供了见解。为促进可复现性，我们的代码将在发表后公开提供。