  Pretraining methods are typically compared by evaluating the accuracy of
linear classifiers, transfer learning performance, or visually inspecting the
representation manifold's (RM) lower-dimensional projections. We show that the
differences between methods can be understood more clearly by investigating the
RM directly, which allows for a more detailed comparison. To this end, we
propose a framework and new metric to measure and compare different RMs. We
also investigate and report on the RM characteristics for various pretraining
methods. These characteristics are measured by applying sequentially larger
local alterations to the input data, using white noise injections and Projected
Gradient Descent (PGD) adversarial attacks, and then tracking each datapoint.
We calculate the total distance moved for each datapoint and the relative
change in distance between successive alterations. We show that self-supervised
methods learn an RM where alterations lead to large but constant size changes,
indicating a smoother RM than fully supervised methods. We then combine these
measurements into one metric, the Representation Manifold Quality Metric
(RMQM), where larger values indicate larger and less variable step sizes, and
show that RMQM correlates positively with performance on downstream tasks.
