1. A method for training an image classification system to classify an input image by minimizing a loss function, wherein the image classification system comprises a first neural network that generates, from a low-resolution image generated from the input image, a respective first score for each of a plurality of object categories that represents a likelihood that the low-resolution image contains an image of an object belonging to the object category, a second neural network that generates, from an initial patch of the input image, a respective second score for each of the object categories that represents a likelihood that the initial patch contains an image of an object belonging to the object category, and an initial patch locator neural network that generates a predicted location of the initial patch of the input image from features of the low-resolution image and from the first scores for the input image, the method comprising: obtaining a first training image, wherein the first training image includes an image of a first object from a first object category; obtaining current parameter values for parameters of the first neural network, parameters of the second neural network, and parameters of the initial patch locator neural network; down-sampling the first training image to generate a low-resolution first training image; processing the low-resolution first training image using the first neural network to generate a plurality of features of the low-resolution first training image and first scores for the low-resolution first training image in accordance with the current values of the parameters of the first neural network; processing the first scores for the low-resolution first training image and the features of the low-resolution first training image using the initial patch locator neural network to generate an initial location of an initial patch of the first training image in accordance with current values of the parameters of the initial patch locator neural network; locally perturbing the initial location to select an adjusted location for the initial patch of the first training image from among a plurality of candidate locations in the first training image; and updating the current values of the parameters of the initial patch locator neural network to generate updated values using the adjusted location, wherein processing the first scores for the low-resolution first training image and the features of the low-resolution first training image using the initial patch locator neural network in accordance with the updated values of the parameters of the initial patch locator neural network generates an alternative predicted location having a smaller distance from the adjusted location than a distance between the predicted location and the adjusted location.