  Recently, deep learning-based algorithms are widely adopted due to the
advantage of being able to establish anomaly detection models without or with
minimal domain knowledge of the task. Instead, to train the artificial neural
network more stable, it should be better to define the appropriate neural
network structure or the loss function. For the training anomaly detection
model, the mean squared error (MSE) function is adopted widely. On the other
hand, the novel loss function, logarithmic mean squared error (LMSE), is
proposed in this paper to train the neural network more stable. This study
covers a variety of comparisons from mathematical comparisons, visualization in
the differential domain for backpropagation, loss convergence in the training
process, and anomaly detection performance. In an overall view, LMSE is
superior to the existing MSE function in terms of strongness of loss
convergence, anomaly detection performance. The LMSE function is expected to be
applicable for training not only the anomaly detection model but also the
general generative neural network.
