  Target encoding plays a central role when learning Convolutional Neural
Networks. In this realm, One-hot encoding is the most prevalent strategy due to
its simplicity. However, this so widespread encoding schema assumes a flat
label space, thus ignoring rich relationships existing among labels that can be
exploited during training. In large-scale datasets, data does not span the full
label space, but instead lies in a low-dimensional output manifold. Following
this observation, we embed the targets into a low-dimensional space,
drastically improving convergence speed while preserving accuracy. Our
contribution is two fold: (i) We show that random projections of the label
space are a valid tool to find such lower dimensional embeddings, boosting
dramatically convergence rates at zero computational cost; and (ii) we propose
a normalized eigenrepresentation of the class manifold that encodes the targets
with minimal information loss, improving the accuracy of random projections
encoding while enjoying the same convergence rates. Experiments on CIFAR-100,
CUB200-2011, Imagenet, and MIT Places demonstrate that the proposed approach
drastically improves convergence speed while reaching very competitive accuracy
rates.
