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.

引入了一种新的模型 ——CIPNN（连续不定概率神经网络），是基于 IPNN 的模型，用于处理离散潜在随机变量。本文提出了新的理论解决了连续潜在随机变量后验的计算问题，创新地提出了基于概率的自编码器 CIPAE，并且提出了一种视觉化方法及进行分类任务，实验结果表明该模型可以无限度地提高分类能力。

连续不定概率神经网络

Continuous Indeterminate Probability Neural Network

We propose a new general model called IPNN - Indeterminate Probability Neural
Network, which combines neural network and probability theory together. In the
classical probability theory, the calculation of probability is based on the
occurrence of events, which is hardly used in current neural networks. In this
paper, we propose a new general probability theory, which is an extension of
classical probability theory, and makes classical probability theory a special
case to our theory. Besides, for our proposed neural network framework, the
output of neural network is defined as probability events, and based on the
statistical analysis of these events, the inference model for classification
task is deduced. IPNN shows new property: It can perform unsupervised
clustering while doing classification. Besides, IPNN is capable of making very
large classification with very small neural network, e.g. model with 100 output
nodes can classify 10 billion categories. Theoretical advantages are reflected
in experimental results.

本文提出了一种新的概率神经网络模型 IPNN，该模型能够将神经网络和概率理论结合起来，并且在分类任务中具有无监督聚类的能力。该模型可以使用很小的神经网络对数十亿个类别进行分类。