Universal Approximation by a Slim Network with Sparse Shortcut Connections
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Over recent years, deep learning has become a mainstream method in machine learning. More advanced networks are being actively developed to solve real-world problems in many important areas. Among successful features of network architectures, shortcut connections are well established to take the outputs of earlier layers as the inputs to later layers, and produce excellent results such as in ResNet and DenseNet. Despite the power of shortcuts, there remain important questions on the underlying mechanism and associated functionalities. For example, will adding shortcuts lead to a more compact structure? How to use shortcuts for an optimal efficiency and capacity of the network model? Along this direction, here we demonstrate that given only one neuron in each layer, the shortcuts can be sparsely placed to let the slim network become an universal approximator. Potentially, our theoretically-guaranteed sparse network model can achieve a learning performance comparable to densely-connected networks on well-known benchmarks.
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