A General Interpretation of Deep Learning by Affine Transform and Region Dividing without Mutual Interference
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This paper mainly deals with the "black-box" problem of deep learning composed of ReLUs with n-dimensional input space, as well as some discussions of sigmoid-unit deep learning. We prove that a region of input space can be transmitted to succeeding layers one by one in the sense of affine transforms; adding a new layer can help to realize the subregion dividing without influencing an excluded region, which is a key distinctive feature of deep leaning. Then constructive proof is given to demonstrate that multi-category data points can be classified by deep learning. Furthermore, we prove that deep learning can approximate an arbitrary continuous function on a closed set of n-dimensional space with arbitrary precision. Finally, generalize some of the conclusions of ReLU deep learning to the case of sigmoid-unit deep learning.
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