  Empirical science of neural scaling laws is a rapidly growing area of
significant importance to the future of machine learning, particularly in the
light of recent breakthroughs achieved by large-scale pre-trained models such
as GPT-3, CLIP and DALL-e. Accurately predicting the neural network performance
with increasing resources such as data, compute and model size provides a more
comprehensive evaluation of different approaches across multiple scales, as
opposed to traditional point-wise comparisons of fixed-size models on
fixed-size benchmarks, and, most importantly, allows for focus on the
best-scaling, and thus most promising in the future, approaches. In this work,
we consider a challenging problem of few-shot learning in image classification,
especially when the target data distribution in the few-shot phase is different
from the source, training, data distribution, in a sense that it includes new
image classes not encountered during training. Our current main goal is to
investigate how the amount of pre-training data affects the few-shot
generalization performance of standard image classifiers. Our key observations
are that (1) such performance improvements are well-approximated by power laws
(linear log-log plots) as the training set size increases, (2) this applies to
both cases of target data coming from either the same or from a different
domain (i.e., new classes) as the training data, and (3) few-shot performance
on new classes converges at a faster rate than the standard classification
performance on previously seen classes. Our findings shed new light on the
relationship between scale and generalization.
