  Quantitative structure-property relationships (QSPRs) aid in understanding
molecular properties as a function of molecular structure. When the correlation
between structure and property weakens, a dataset is described as "rough," but
this characteristic is partly a function of the chosen representation. Among
possible molecular representations are those from recently-developed
"foundation models" for chemistry which learn molecular representation from
unlabeled samples via self-supervision. However, the performance of these
pretrained representations on property prediction benchmarks is mixed when
compared to baseline approaches. We sought to understand these trends in terms
of the roughness of the underlying QSPR surfaces. We introduce a reformulation
of the roughness index (ROGI), ROGI-XD, to enable comparison of ROGI values
across representations and evaluate various pretrained representations and
those constructed by simple fingerprints and descriptors. We show that
pretrained representations do not produce smoother QSPR surfaces, in agreement
with previous empirical results of model accuracy. Our findings suggest that
imposing stronger assumptions of smoothness with respect to molecular structure
during model pretraining can aid in the downstream generation of smoother QSPR
surfaces.
