Activation functions play an essential role in neural networks. They provide the non-linearity for the networks. Therefore, their properties are important for neural networks' accuracy and running performance. In this paper, we present a novel signed and truncated logarithm function as activation function. The proposed activation function has significantly better mathematical properties, such as being odd function, monotone, differentiable, having unbounded value range, and a continuous nonzero gradient. These properties make it an excellent choice as an activation function. We compare it with other well-known activation functions in several well-known neural networks. The results confirm that it is the state-of-the-art. The suggested activation function can be applied in a large range of neural networks where activation functions are necessary.

翻译：激活函数在神经网络中起着至关重要的作用，它们为网络提供非线性特性。因此，激活函数的性质对神经网络的精度和运行性能至关重要。本文提出了一种新颖的带符号截断对数函数作为激活函数。该激活函数具有显著更优的数学性质，例如奇函数、单调性、可微性、无界值域以及连续非零梯度。这些性质使其成为激活函数的理想选择。我们将其与多个知名神经网络中的其他经典激活函数进行对比，实验结果证实其达到了当前最优水平。该激活函数可广泛应用于任何需要激活函数的神经网络场景。