  We present a latent variable model for classification that provides a novel
probabilistic interpretation of neural network softmax classifiers. We derive a
variational objective to train the model, analogous to the evidence lower bound
(ELBO) used to train variational auto-encoders, that generalises the softmax
cross-entropy loss. Treating inputs to the softmax layer as samples of a latent
variable, our abstracted perspective reveals a potential inconsistency between
their anticipated distribution, required for accurate label predictions, and
their empirical distribution found in practice. We augment the variational
objective to mitigate such inconsistency and induce a chosen latent
distribution, instead of the implicit assumption found in a standard softmax
layer. Overall, we provide new theoretical insight into the inner workings of
widely-used softmax classifiers. Empirical evaluation on image and text
classification datasets demonstrates that our proposed approach, variational
classification, maintains classification accuracy while the reshaped latent
space improves other desirable properties of a classifier, such as calibration,
adversarial robustness, robustness to distribution shift and sample efficiency
useful in low data settings.
