Hierarchical Feature Engineering

It is instructive to examine the activations of the filters created by real-world images in different layers. The activations of the filters in the early layers are low-level features like edges, whereas those in later layers put together these low-level features. For example, a mid-level feature might put together edges to create a hexagon, whereas a higher-level feature might put together the mid-level hexagons to create a honeycomb. It is fairly easy to see why a low-level filter might detect edges. Consider a situation in which the color of the image changes along an edge.As a result, the difference between neighboring pixel values will be non-zero only across the edge. This can be achieved by choosing the appropriate weights in the corresponding low-level filter. Note that the filter to detect a horizontal edge will not be the same as that to detect a vertical edge. This brings us back to Hubel and Weisel’s experiments in which different neurons in the cat’s visual cortex were activated by different edges. Examples of filters detecting horizontal and vertical edges are illustrated in Figure below. The next layer filter works on the hidden features and therefore it is harder to interpret. Nevertheless, the next layer filter is able to detect a rectangle by combining the horizontal and vertical edges.


The power of convolutional neural networks rests in the ability to put together these primitive shapes into more complex shapes layer by layer. Note that it is impossible for the first convolution layer to learn any feature that is larger than $F1×F1$ pixels, where the value of $F1$ is typically a small number like 3 or 5. However, the next convolution layer will be able to put together many of these patches together to create a feature from an area of the image that is larger. The primitive features learned in earlier layers are put together in a semantically coherent way to learn increasingly complex and interpretable visual features. The choice of learned features is affected by how backpropagation adapts the features to the needs of the loss function at hand. For example, if an application is training to classify images as cars, the approach might learn to put together arcs to create a circle, and then it might put together circles with other shapes to create a car wheel. All this is enabled by the hierarchical features of a deep network.

Recent ImageNet competitions have demonstrated that much of the power in image recognition lies in increased depth of the network. Not having enough layers effectively prevents the network from learning the hierarchical regularities in the image that are combined to create its semantically relevant components. Another important observation is that the nature of the features learned will be sensitive to the specific data set at hand. For example, the features learned to recognize trucks will be different from those learned to recognize carrots.However, some data sets (like ImageNet) are diverse enough that the features learned by training on these data sets have general-purpose significance across many applications.

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