  The impressive success of recent deep neural network (DNN)-based systems is
significantly influenced by the high-quality datasets used in training.
However, the effects of the datasets, especially how they interact with each
other, remain underexplored. We propose a state-vector framework to enable
rigorous studies in this direction. This framework uses idealized probing test
results as the bases of a vector space. This framework allows us to quantify
the effects of both standalone and interacting datasets. We show that the
significant effects of some commonly-used language understanding datasets are
characteristic and are concentrated on a few linguistic dimensions.
Additionally, we observe some ``spill-over'' effects: the datasets could impact
the models along dimensions that may seem unrelated to the intended tasks. Our
state-vector framework paves the way for a systematic understanding of the
dataset effects, a crucial component in responsible and robust model
development.
