Bilateral sensitivity analysis: a better understanding of a neural network

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Research Article

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International Journal of Machine Learning and Cybernetics


A model-independent sensitivity analysis for (deep) neural network, Bilateral sensitivity analysis (BiSA), is proposed to measure the relationship or dependency between neurons and layers. For any feed-forward neural networks including deep networks, we have defined the BiSA between a pair of layers as well as the same between any pair neurons in different layers. This sensitivity can quantify the influence or contribution from any layer to any other higher level layer. It provides a helpful tool to interpret the learned model. The BiSA can also measure the influence from any neuron to another neuron in a subsequent layer and it is critical to analyze the relationship between neurons in different layers. Then the BiSA from any input to any output of the network is easily defined to assess the strength of connection between the inputs and outputs. We have applied BiSA to characterize the well connectivity in oil fields—a very important and challenging problem in reservoir engineering. Given a network trained by Water Injection Rates and Liquid Production Rates data, the well connectivity can be efficiently discovered through BiSA. The empirical results verify the effectiveness of BiSA. Our comparison with exiting methods demonstrates the robustness and the superior performance. Besides, we also investigate the effectiveness of BiSA for a feature selection task using a deep neural network. The experimental results on MNIST data set demonstrate a satisfactory performance of BiSA on this issue with 1,536,640,000 parameters in the neural network.

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