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Is there any good paper (sort of best practices) that experimentally explains what happens to CNNs when the training and testing data follow different distribution. This is for the case when CNN is not overfitting but its testing accuracy is low.

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The thing is if your testing data is significantly different from the training data you cannot explain testing data with training data. As a result, there cannot be an experiment that shows such correlation without known correlation between training and testing data. My suggestion is, if you are in this situation, split your training data into training/validation thus guaranteeing that both distributions match.

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