The power law has been observed in the degree distributions of many biological neural networks. Sparse deep neural networks, which learn an economical representation from the data, resemble biological neural networks in many ways. In this paper, we study if these artificial networks also exhibit properties of the power law. Experimental results on two popular deep learning models, namely, multilayer perceptrons and convolutional neural networks, are affirmative. The power law is also naturally related to preferential attachment. To study the dynamical properties of deep networks in continual learning, we propose an internal preferential attachment model to explain how the network topology evolves. Experimental results show that with the arrival of a new task, the new connections made follow this preferential attachment process.
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