论文标题
部分可观测时空混沌系统的无模型预测
Understanding out-of-distribution accuracies through quantifying difficulty of test samples
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Existing works show that although modern neural networks achieve remarkable generalization performance on the in-distribution (ID) dataset, the accuracy drops significantly on the out-of-distribution (OOD) datasets \cite{recht2018cifar, recht2019imagenet}. To understand why a variety of models consistently make more mistakes in the OOD datasets, we propose a new metric to quantify the difficulty of the test images (either ID or OOD) that depends on the interaction of the training dataset and the model. In particular, we introduce \textit{confusion score} as a label-free measure of image difficulty which quantifies the amount of disagreement on a given test image based on the class conditional probabilities estimated by an ensemble of trained models. Using the confusion score, we investigate CIFAR-10 and its OOD derivatives. Next, by partitioning test and OOD datasets via their confusion scores, we predict the relationship between ID and OOD accuracies for various architectures. This allows us to obtain an estimator of the OOD accuracy of a given model only using ID test labels. Our observations indicate that the biggest contribution to the accuracy drop comes from images with high confusion scores. Upon further inspection, we report on the nature of the misclassified images grouped by their confusion scores: \textit{(i)} images with high confusion scores contain \textit{weak spurious correlations} that appear in multiple classes in the training data and lack clear \textit{class-specific features}, and \textit{(ii)} images with low confusion scores exhibit spurious correlations that belong to another class, namely \textit{class-specific spurious correlations}.