We discuss probabilistic neural networks for unsupervised learning 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 more traditional models such as Restricted Boltzmann Machines.

翻译：我们讨论了一种用于无监督学习的概率神经网络，该网络采用固定的内部表示，作为机器理解的模型。这里的理解旨在将数据映射到一种已有的表示上，这种表示编码了特征空间的先验组织。我们通过要求内部表示满足最大相关性原则以及关于不同特征如何组合的最大无知性原则，推导出该内部表示。我们证明，当隐藏单元为二元变量时，这两个原则确定了一个唯一模型——层次特征模型（HFM）——该模型完全可解，并能从特征角度提供自然的解释。我们论证，具有这种架构的学习机器拥有若干有趣特性，例如表示相对于参数和数据的连续性、控制压缩水平的可能性，以及支持超越泛化的功能。我们通过大量数值实验探索了该模型的行为，并论证，内部表示固定的模型重现了一种学习模式，该模式在性质上不同于受限玻尔兹曼机等更传统模型的学习模式。