Modern deep learning is primarily an experimental science, in which empirical advances occasionally come at the expense of probabilistic rigor. Here we focus on one such example; namely the use of the categorical cross-entropy loss to model data that is not strictly categorical, but rather takes values on the simplex. This practice is standard in neural network architectures with label smoothing and actor-mimic reinforcement learning, amongst others. Drawing on the recently discovered {continuous-categorical} distribution, we propose probabilistically-inspired alternatives to these models, providing an approach that is a more principled and theoretically appealing. Through careful experimentation, including an ablation study, we identify the potential for outperformance in these models, thereby highlighting the importance of a proper probabilistic treatment, as well as illustrating some of the failure modes thereof.