  Modern neural architectures for classification tasks are trained using the
cross-entropy loss, which is widely believed to be empirically superior to the
square loss. In this work we provide evidence indicating that this belief may
not be well-founded. We explore several major neural architectures and a range
of standard benchmark datasets for NLP, automatic speech recognition (ASR) and
computer vision tasks to show that these architectures, with the same
hyper-parameter settings as reported in the literature, perform comparably or
better when trained with the square loss, even after equalizing computational
resources. Indeed, we observe that the square loss produces better results in
the dominant majority of NLP and ASR experiments. Cross-entropy appears to have
a slight edge on computer vision tasks.
  We argue that there is little compelling empirical or theoretical evidence
indicating a clear-cut advantage to the cross-entropy loss. Indeed, in our
experiments, performance on nearly all non-vision tasks can be improved,
sometimes significantly, by switching to the square loss. Furthermore, training
with square loss appears to be less sensitive to the randomness in
initialization. We posit that training using the square loss for classification
needs to be a part of best practices of modern deep learning on equal footing
with cross-entropy.
