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Recently, neural networks in machine learning use rectified linear units(ReLUs) in early processing layers for better performance. Training thesestructures sometimes results in "dying ReLU units" with near-zero outputs. Wefirst explore this condition via simulation using the CIFAR-10 dataset andvariants of two popular convolutive neural network architectures. Ourexplorations show that the output activation probability Pr[y>0] is generallyless than 0.5 at system convergence for layers that do not employ skipconnections, and this activation probability tends to decrease as oneprogresses from input layer to output layer. Employing a simplified model of asingle ReLU unit trained by a variant of error backpropagation, we then performa statistical convergence analysis to explore the model's evolutionarybehavior. Our analysis describes the potentially-slower convergence speeds ofdying ReLU units, and this issue can occur regardless of how the weights areinitialized.

Why ReLU Units Sometimes Die: Analysis of Single-Unit Error Backpropagation in Neural Networks