  We explore and expand the $\textit{Soft Nearest Neighbor Loss}$ to measure
the $\textit{entanglement}$ of class manifolds in representation space: i.e.,
how close pairs of points from the same class are relative to pairs of points
from different classes. We demonstrate several use cases of the loss. As an
analytical tool, it provides insights into the evolution of class similarity
structures during learning. Surprisingly, we find that $\textit{maximizing}$
the entanglement of representations of different classes in the hidden layers
is beneficial for discrimination in the final layer, possibly because it
encourages representations to identify class-independent similarity structures.
Maximizing the soft nearest neighbor loss in the hidden layers leads not only
to improved generalization but also to better-calibrated estimates of
uncertainty on outlier data. Data that is not from the training distribution
can be recognized by observing that in the hidden layers, it has fewer than the
normal number of neighbors from the predicted class.
