  Within the world of machine learning there exists a wide range of different
methods with respective advantages and applications. This paper seeks to
present and discuss one such method, namely Convolutional Neural Networks
(CNNs). CNNs are deep neural networks that use a special linear operation
called convolution. This operation represents a key and distinctive element of
CNNs, and will therefore be the focus of this method paper. The discussion
starts with the theoretical foundations that underlie convolutions and CNNs.
Then, the discussion proceeds to discuss some improvements and augmentations
that can be made to adapt the method to estimate a wider set of function
classes. The paper mainly investigates two ways of improving the method: by
using locally connected layers, which can make the network less invariant to
translation, and tiled convolution, which allows for the learning of more
complex invariances than standard convolution. Furthermore, the use of the Fast
Fourier Transform can improve the computational efficiency of convolution.
Subsequently, this paper discusses two applications of convolution that have
proven to be very effective in practice. First, the YOLO architecture is a
state of the art neural network for image object classification, which
accurately predicts bounding boxes around objects in images. Second, tumor
detection in mammography may be performed using CNNs, accomplishing 7.2% higher
specificity than actual doctors with only .3% less sensitivity. Finally, the
invention of technology that outperforms humans in different fields also raises
certain ethical and regulatory questions that are briefly discussed.
