Redundancy in active paths of deep networks: a random active path model
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Deep learning has become a powerful and popular tool for a variety of machine learning tasks. However, it is extremely challenging to understand the mechanism of deep learning from a theoretical perspective. In this work, we study robustness of a deep network in its generalization capability against removal of a certain number of connections between layers. A critical value of this number is observed to separate a robust (redundant) regime from a sensitive regime. This empirical behavior is captured qualitatively by a random active path model, where the path from input to output is randomly and independently constructed. The empirical critical value corresponds to termination of a paramagnetic phase in the random active path model. Furthermore, this model provides us qualitative understandings about dropconnect probability commonly used in the dropconnect algorithm and its relationship with the redundancy phenomenon. In addition, we combine the dropconnect and the random feedback alignment for feedforward and backward pass in a deep network training respectively, and observe fast learning and improved test performance in classifying a benchmark handwritten digits dataset.
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