We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori} organisation of the feature space. We derive the internal representation by requiring that it satisfies the principles of maximal relevance and of maximal ignorance about how different features are combined. We show that, when hidden units are binary variables, these two principles identify a unique model -- the Hierarchical Feature Model (HFM) -- which is fully solvable and provides a natural interpretation in terms of features. We argue that learning machines with this architecture enjoy a number of interesting properties, like the continuity of the representation with respect to changes in parameters and data, the possibility to control the level of compression and the ability to support functions that go beyond generalisation. We explore the behaviour of the model with extensive numerical experiments and argue that models where the internal representation is fixed reproduce a learning modality which is qualitatively different from that of traditional models such as Restricted Boltzmann Machines.

翻译：我们讨论了具有固定内部表示的概率神经网络作为机器理解模型。这里的理解是指将数据映射到已有的表示上，该表示编码了特征空间的一种先验组织。我们通过要求内部表示满足最大相关性原则和对不同特征组合方式的最大无知原则来推导该表示。研究表明，当隐藏单元为二元变量时，这两个原则唯一确定了一个模型——层次特征模型——该模型完全可解，并能从特征角度提供自然的解释。我们认为，具有这种架构的学习机器具备一系列有趣性质，例如表示对参数和数据的连续依赖性、可控的压缩程度，以及支持超越泛化功能的潜力。我们通过大量数值实验探索了该模型的行为，并论证了具有固定内部表示的模型所复现的学习模式，在本质上不同于受限玻尔兹曼机等传统模型。