A Detailed Accounting of Error in Neural Networks: Applications to Electromagnetics

Barger, Maria

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A Detailed Accounting of Error in Neural Networks: Applications to Electromagnetics

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Neural networks are a widely utilized tool whose usefulness has been demonstrated in many real-world problems. However, we sometimes see a disconnect between mathematical theory and the practice of applying neural networks. Here we seek to understand this disconnect and study some examples of error arising from the mismatch between theory and practice. Our work connects classical analysis techniques such as the Kalman Filter, domain knowledge of neural network applications to electromagnetic signal processing, a Maximum Likelihood Estimator based upon the electromagnetic application, and neural network theory in order to identify and mitigate subtle sources of error in the process of constructing and training neural networks. The main contributions of our research are four key results showing errors regarding the problem of source localization for electromagnetic signals and how to mitigate them. The first result shows that normalization of electromagnetic signals is necessary but not sufficient to prevent our neural networks from data snooping during training. The second result shows an example of our neural networks performing well only on noise levels seen in training and also shows that they must be trained on various noise levels to be useful in real-world applications. The third result combines the Kalman Filter with neural network predictions in order to mitigate errors in predictions made by networks not supplemented by the Kalman Filter. Finally, the fourth result highlights the importance of domain knowledge in our network training so that our network does not become over-reliant on atmospheric data it will not have access to in real-world testing.

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