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I was following the following article with regards to doing transfer learning:

https://blog.keras.io/building-powerful-image-classification-models-using-very-little-data.html

In the section, Using the bottleneck features of a pre-trained network: 90% accuracy in a minute, the authors mentioned that: "Note that this prevents us from using data augmentation"

I am not very clear about this; is there a rule that discourages the use of data augmentation when the pre-trained model is totally frozen?

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No, you can definitely use data augmentation when the layers of the pre-trained model are frozen.

In this article, the author refers to the size of VGG16 which is quite a large CNN. Also, he trains the model on his CPU which slows down training even more. Therefore, he does not want to use data augmentation, as that would increase the training time even more:

Running VGG16 is expensive, especially if you're working on CPU, and we want to only do it once. Note that this prevents us from using data augmentation.

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