The Softmax operation is modified to the function below. In original Softmax, for the model to be unsure, the model must learn to output e.g. By using Relaxed Softmax, this becomes as easy as predicting an appropriately small single α value.

In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation, two fields that fall into the framework of learning from Positive and Unlabeled data. In this paper, we stress the different drawbacks of the current family of softmax losses and sampling schemes when applied in a Positive and Unlabeled learning setup. We propose both a Relaxed Softmax loss (RS) and a new negative sampling scheme based on Boltzmann formulation. We show that the new training objective is better suited for the tasks of density estimation, item similarity and next-event prediction by driving uplifts in performance on textual and recommendation datasets against classical softmax.