  Deep learning (DL) creates impactful advances following a virtuous recipe:
model architecture search, creating large training data sets, and scaling
computation. It is widely believed that growing training sets and models should
improve accuracy and result in better products. As DL application domains grow,
we would like a deeper understanding of the relationships between training set
size, computational scale, and model accuracy improvements to advance the
state-of-the-art.
  This paper presents a large scale empirical characterization of
generalization error and model size growth as training sets grow. We introduce
a methodology for this measurement and test four machine learning domains:
machine translation, language modeling, image processing, and speech
recognition. Our empirical results show power-law generalization error scaling
across a breadth of factors, resulting in power-law exponents---the "steepness"
of the learning curve---yet to be explained by theoretical work. Further, model
improvements only shift the error but do not appear to affect the power-law
exponent. We also show that model size scales sublinearly with data size. These
scaling relationships have significant implications on deep learning research,
practice, and systems. They can assist model debugging, setting accuracy
targets, and decisions about data set growth. They can also guide computing
system design and underscore the importance of continued computational scaling.
