Given a CNN trained on MNIST, can I easily build a similar network that recognized those digits anywhere in a 50×50 image?

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Phrased another way, if I had a CNN that recognized 28×28 MNIST digits, is there a known method to classify those MNIST digits if they appeared anywhere within a 50×50 image (the digits themselves would still be 28×28).

— Assume the last layer is fully connected + softmax. The convolutional layers should remain unchanged, so this question breaks down to easily creating a dense layer that works for 50×50 from the one that worked with 28×28.

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Why I think this is important: We can achieve more specific labeling with smaller image sizes, cropping out things like eyes and noses and being able to recognize them in new places in an image. Also, this would potentially reduce the amount and variety of training data needed (we wouldn’t have to create new 50×50 images with the 28×28 images tiled in different locations).