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A simple way I can think of to detect OOD samples is to treat them like another class in a multiclass classification problem. For example, with MNIST, we would modify the network to predict another class in addition to the 10 digits. So logit 11 represents OOD. Then we train the network with supervised learning where the OOD data has the OOD class label. This assumes that we have access to some OOD data. Does anyone know a paper which does this?

Learning Confidence for Out-of-Distribution Detection in Neural Networks adds an OOD prediction branch to the neural network. However, that method doesn't assume access to OOD data during training, so their training is different than what I described.

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What you propose is just supervised classification. However, this kind of approach will tend to fail on novel anomalies/outliers. Because the supervised learning will just learn to discriminate the known outliers from the known inliers. This is one of the major reasons to use an unsupervised / one-class approach using only the normal data. This is explained in https://www.flair-tech.com/en/why-anomaly-detection-is-not-binary-classification/

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