  In machine learning, we traditionally evaluate the performance of a single
model, averaged over a collection of test inputs. In this work, we propose a
new approach: we measure the performance of a collection of models when
evaluated on a $\textit{single input point}$. Specifically, we study a point's
$\textit{profile}$: the relationship between models' average performance on the
test distribution and their pointwise performance on this individual point. We
find that profiles can yield new insights into the structure of both models and
data -- in and out-of-distribution. For example, we empirically show that real
data distributions consist of points with qualitatively different profiles. On
one hand, there are "compatible" points with strong correlation between the
pointwise and average performance. On the other hand, there are points with
weak and even $\textit{negative}$ correlation: cases where improving overall
model accuracy actually $\textit{hurts}$ performance on these inputs. We prove
that these experimental observations are inconsistent with the predictions of
several simplified models of learning proposed in prior work. As an
application, we use profiles to construct a dataset we call CIFAR-10-NEG: a
subset of CINIC-10 such that for standard models, accuracy on CIFAR-10-NEG is
$\textit{negatively correlated}$ with accuracy on CIFAR-10 test. This
illustrates, for the first time, an OOD dataset that completely inverts
"accuracy-on-the-line" (Miller, Taori, Raghunathan, Sagawa, Koh, Shankar,
Liang, Carmon, and Schmidt 2021)
