Making predictions at every time step

If I want to make a neural network that make prediction at every time step, instead of making one prediction, how should I approach this problem, for example, if I am doing image classification, then instead of asking my neural network to predict the class for an entire image, I show my neural network only a part of image, and get a prediction, then backpropagate, update weights, in the next time step, I show neural network a bigger part of image, get prediction, then backpropagate, update weights, and so on, and at the last time step, I show my neural network entire image.

Because we are sometimes able to predict class of image correctly by seeing part of image only, without seeing the entire picture.

Is there any term for this type of neural network training, or any example that work like this?