Radial Prediction Layer

For a broad variety of critical applications, it is essential to know how confident a classification prediction is. In this paper, we discuss the drawbacks of softmax to calculate class probabilities and to handle uncertainty in Bayesian neural networks. We introduce a new kind of prediction layer called radial prediction layer (RPL) to overcome these issues. In contrast to the softmax classification, RPL is based on the open-world assumption. Therefore, the class prediction probabilities are much more meaningful to assess the uncertainty concerning the novelty of the input. We show that neural networks with RPLs can be learned in the same way as neural networks using softmax. On a 2D toy data set (spiral data), we demonstrate the fundamental principles and advantages. On the real-world ImageNet data set, we show that the open-world properties are beneficially fulfilled. Additionally, we show that RPLs are less sensible to adversarial attacks on the MNIST data set. Due to its features, we expect RPL to be beneficial in a broad variety of applications, especially in critical environments, such as medicine or autonomous driving.