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For the transfer learning do we need to have same input image size of target model as source model? for example my source model is trained on 100x100 input images and target model is low resolution images and are of size 50x50.

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No. For example, powerful models trained on Imagenet are often reused in all sorts of diverse settings and tasks of wildly different input size.

Of course it can only help to have the target domain be as similar as possible to the source domain.

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