this key characteristic gives convnets two interesting propertiesthe patterns they learn are translation invariant after learning certain pattern in the lower-right corner of picturea convnet can recognize it anywherefor examplein the upper-left corner densely connected network would have to learn the pattern anew if it appeared at new location this makes convnets data efficient when processing images (because the visual world is fundamentally translation invariant)they need fewer training samples to learn representations that have generalization power they can learn spatial hierarchies of patterns (see figure first convolution layer will learn small local patterns such as edgesa second convolution layer will learn larger patterns made of the features of the first layersand so on this allows convnets to efficiently learn increasingly complex and abstract visual concepts (because the visual world is fundamentally spatially hierarchical"catfigure the visual world forms spat ial hierarchy of visual moduleshyperlocal edges combine int local object such as eyes or earswhich combine int high-level concept such as cat convolutions operate over tensorscalled feature mapswith two spatial axes (height and widthas well as depth axis (also called the channels axisfor an rgb imagethe dimension of the depth axis is because the image has three color channelsredgreenand blue for black-and-white picturelike the mnist digitsthe depth is (levels of graythe convolution operation extracts patches from its input feature map and applies the same transformation to all of these patchesproducing an output feature map this output feature map is still tensorit has width and height its depth can be arbitrarybecause the output depth is parameter of the layerand the licensed to