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.

翻译：近年来，基于深度学习的算法因能够在不依赖或极少依赖任务领域知识的情况下建立异常检测模型而被广泛采用。然而，为了更稳定地训练人工神经网络，定义合适的网络结构或损失函数至关重要。在异常检测模型的训练中，均方误差函数被广泛使用。另一方面，本文提出了一种新型损失函数——对数均方误差，以使神经网络训练更加稳定。本研究涵盖了从数学比较、反向传播微分域的可视化、训练过程中的损失收敛性到异常检测性能的多种对比。总体而言，LMSE在损失收敛的强度以及异常检测性能方面优于现有的MSE函数。预计LMSE函数不仅适用于异常检测模型的训练，还可用于一般生成神经网络的训练。