Semantic and Generalized Entropy Loss Functions for Semi-Supervised Deep Learning

The increasing size of modern datasets combined with the difficulty of obtaining real label information (e.g., class) has made semi-supervised learning a problem of considerable practical importance in modern data analysis. Semi-supervised learning is supervised learning with additional information on the distribution of the examples or, simultaneously, an extension of unsupervised learning guided by some constraints. In this article we present a methodology that bridges between artificial neural network output vectors and logical constraints. In order to do this, we present a semantic loss function and a generalized entropy loss function (Rényi entropy) that capture how close the neural network is to satisfying the constraints on its output. Our methods are intended to be generally applicable and compatible with any feedforward neural network. Therefore, the semantic loss and generalized entropy loss are simply a regularization term that can be directly plugged into an existing loss function. We evaluate our methodology over an artificially simulated dataset and two commonly used benchmark datasets which are MNIST and Fashion-MNIST to assess the relation between the analyzed loss functions and the influence of the various input and tuning parameters on the classification accuracy. The experimental evaluation shows that both losses effectively guide the learner to achieve (near-) state-of-the-art results on semi-supervised multiclass classification.