Convolutional neural networks utilize a hierarchy of neural network layers. The statistical aspects of information concentration in successive layers can bring an insight into the feature abstraction process. We analyze the saliency maps of these layers from the perspective of semiotics, also known as the study of signs and sign-using behavior. In computational semiotics, this aggregation operation (known as superization) is accompanied by a decrease of spatial entropy: signs are aggregated into supersign. Using spatial entropy, we compute the information content of the saliency maps and study the superization processes which take place between successive layers of the network. In our experiments, we visualize the superization process and show how the obtained knowledge can be used to explain the neural decision model. In addition, we attempt to optimize the architecture of the neural model employing a semiotic greedy technique. To the extent of our knowledge, this is the first application of computational semiotics in the analysis and interpretation of deep neural networks.

The information bottleneck principle was recently proposed as a theory meant to explain some of the training dynamics of deep neural architectures. Via information plane analysis, patterns start to emerge in this framework, where two phases can be distinguished: fitting and compression. We take a step further and study the behaviour of the spatial entropy characterizing the layers of convolutional neural networks (CNNs), in relation to the information bottleneck theory. We observe pattern formations which resemble the information bottleneck fitting and compression phases. From the perspective of semiotics, also known as the study of signs and sign-using behavior, the saliency maps of CNN’s layers exhibit aggregations: signs are aggregated into supersigns and this process is called semiotic superization. Superization can be characterized by a decrease of entropy and interpreted as information concentration. We discuss the information bottleneck principle from the perspective of semiotic superization and discover very interesting analogies related to the informational adaptation of the model. In a practical application, we introduce a modification of the CNN training process: we progressively freeze the layers with small entropy variation of their saliency map representation. Such layers can be stopped earlier from training without a significant impact on the performance (the accuracy) of the network, connecting the entropy evolution through time with the training dynamics of a network.