The current progress in image recognition is made by changing the approach from a classic feature selection (shallow learning algorithm) to no feature selection (deep learning), due to the mathematical properties of convolutional neural networks. Their ability to capture the same information using a smaller number of parameters was partially caused by their shift-invariance property.
The main reason behind this success was developing faster learning algorithms than more mathematically accurate ones, so less attention is put on developing another property invariant neural nets.
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