  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 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.
