A simple probabilistic neural network for machine understanding
This work addresses the challenge of developing interpretable and stable learning models for machine understanding, though it appears incremental as it builds on existing probabilistic frameworks.
The authors tackled the problem of machine understanding by proposing a probabilistic neural network with a fixed internal representation, derived from principles of maximal relevance and maximal ignorance, which results in the Hierarchical Feature Model (HFM) that is fully solvable and exhibits properties like continuity and controlled compression.
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.