Assessing Model Out-of-distribution Generalization with Softmax Prediction Probability Baselines and A Correlation Method

Weijie Tu, Weijian Deng, Tom Gedeon, Liang Zheng

Abstract: This paper studies the use of Softmax prediction to assess model generalization under distribution shift. Specifically, given an out-of distribution (OOD) test set and a pool of classifiers, we aim to develop a Softmax prediction-based measure which has a monotonic relationship with OOD generalization performance. We first show existing uncertainty measures (e.g., entropy and maximum Softmax prediction) are fairly useful of predicting generalization in some OOD scenarios. We then move ahead with proposing a new measure, Softmax Correlation (SoftmaxCorr). To obtain the SoftmaxCorr score for a classifier, we compute the class-class correlation matrix from all the Softmax vectors in a test set, and then its cosine similarity with an identity matrix. We show that the class-class correlation matrix reveals significant knowledge about the confusion matrix: its high similarity with the identity matrix means predictions have low confusion (uncertainty) and evenly cover all classes, and vice versa. Across three setups including ImageNet, CIFAR-10, and WILDS, we show that SoftmaxCorr is well predictive of model accuracy on both in-distribution and OOD datasets.

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