This paper introduces a general model called CIPNN - Continuous Indeterminate Probability Neural Network, and this model is based on IPNN, which is used for discrete latent random variables. Currently, posterior of continuous latent variables is regarded as intractable, with the new theory proposed by IPNN this problem can be solved. Our contributions are Four-fold. First, we derive the analytical solution of the posterior calculation of continuous latent random variables and propose a general classification model (CIPNN). Second, we propose a general auto-encoder called CIPAE - Continuous Indeterminate Probability Auto-Encoder, the decoder part is not a neural network and uses a fully probabilistic inference model for the first time. Third, we propose a new method to visualize the latent random variables, we use one of N dimensional latent variables as a decoder to reconstruct the input image, which can work even for classification tasks, in this way, we can see what each latent variable has learned. Fourth, IPNN has shown great classification capability, CIPNN has pushed this classification capability to infinity. Theoretical advantages are reflected in experimental results.

翻译：本文提出了一种名为CIPNN（连续不确定概率神经网络）的通用模型，该模型基于用于离散潜随机变量的IPNN。目前，连续潜变量的后验被认为难以处理，而IPNN提出的新理论可解决此问题。我们的贡献包含四个方面：首先，推导了连续潜随机变量后验计算的解析解，并提出了通用分类模型CIPNN；其次，提出了一种名为CIPAE（连续不确定概率自编码器）的通用自编码器，其解码器部分非神经网络，并首次采用完全概率推理模型；第三，提出了一种潜随机变量的可视化新方法，利用N维潜变量中的某一维作为解码器重构输入图像，该方法甚至能适用于分类任务，从而可观察每个潜变量学习到的内容；第四，IPNN已展现出强大的分类能力，而CIPNN将这种分类能力提升至无穷。理论优势在实验结果中得到了充分体现。