  We find that the way we choose to represent data labels can have a profound
effect on the quality of trained models. For example, training an image
classifier to regress audio labels rather than traditional categorical
probabilities produces a more reliable classification. This result is
surprising, considering that audio labels are more complex than simpler
numerical probabilities or text. We hypothesize that high dimensional, high
entropy label representations are generally more useful because they provide a
stronger error signal. We support this hypothesis with evidence from various
label representations including constant matrices, spectrograms, shuffled
spectrograms, Gaussian mixtures, and uniform random matrices of various
dimensionalities. Our experiments reveal that high dimensional, high entropy
labels achieve comparable accuracy to text (categorical) labels on the standard
image classification task, but features learned through our label
representations exhibit more robustness under various adversarial attacks and
better effectiveness with a limited amount of training data. These results
suggest that label representation may play a more important role than
previously thought. The project website is at
\url{https://www.creativemachineslab.com/label-representation.html}.
