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Transfer learning makes sense when the data in training for task A is quite large and that of task B is relatively smaller.
By getting trained on such vast amounts of data and showing excellent performance on its test data, this implies that the neural network has a good knowledge of extracting useful features from the input images. This is essential and powerful for achieving a task.
Now that we have such powerful features from these layers (whose weights from task A are frozen), we just need to make use of these extracted features to achieve task B. So, these features from frozen layers are fed to the new layers, and the parameters for these layers are trained on the data of task B.
So basically, we store the knowledge from the previous task in the form of the weights of the frozen layers (called pre-training). Then we make the neural network task B-specific by training (called fine-tuning) the latter layers on the new data.
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