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We present a Monte Carlo approach for studying chemical feature distributionsof molecules without training a machine learning model or performing exhaustiveenumeration. The algorithm generates molecules with predefined similarity to agiven one for any representation. It serves as a diagnostic tool to understandwhich molecules are grouped in feature space and to identify shortcomings ofrepresentations and embeddings from unsupervised learning. In this work, wefirst study clusters surrounding chosen molecules and demonstrate that commonrepresentations do not yield a constant density of molecules in feature space,with possible implications for learning behavior. Next, we observe a connectionbetween representations and properties: a linear correlation between theproperty value of a central molecule and the average radial slope of thatproperty in chemical space. Molecules with extremal property values have thelargest property derivative values in chemical space, which provides a route toimprove the data efficiency of a representation by tailoring it towards a givenproperty. Finally, we demonstrate applications for sampling molecules withspecified metric-dependent distributions to generate molecules biased towardgraph spaces of interest.

Understanding Representations by Exploring Galaxies in Chemical Space