  Self-supervised speech representations can hugely benefit downstream speech
technologies, yet the properties that make them useful are still poorly
understood. Two candidate properties related to the geometry of the
representation space have been hypothesized to correlate well with downstream
tasks: (1) the degree of orthogonality between the subspaces spanned by the
speaker centroids and phone centroids, and (2) the isotropy of the space, i.e.,
the degree to which all dimensions are effectively utilized. To study them, we
introduce a new measure, Cumulative Residual Variance (CRV), which can be used
to assess both properties. Using linear classifiers for speaker and phone ID to
probe the representations of six different self-supervised models and two
untrained baselines, we ask whether either orthogonality or isotropy correlate
with linear probing accuracy. We find that both measures correlate with
phonetic probing accuracy, though our results on isotropy are more nuanced.
