We observed an exponential relationship between the HAC and the near-neighborhood size for GDB-12 (Figure ). Although the vocabulary set used for creating GDB-12 is smaller than the vocabulary set, V , used to train the transformer models, the behaviour of trained transformer models follow the same trend as shown by GDB-12 for larger HAC, with an approximate linear slope of 0.10 and intercept of 0.55 for both GDB-12 and TTD for HAC 13-36 (i.e. neighborhood size ≈ 10 0.10 HAC+0.55 ). This suggests that, while our sampling remains a lower bound on the full local chemical space, it is approximately as complete as the enumerated near-neighborhood for the GDB-12 database. More approximations of the neighborhood size for different similarity thresholds can be found in Figure in Appendix C. : Average neighborhood size (y-axis in log scale), defined by a similarity threshold of 0.8, to a source compound grouped by their number of heavy atoms (xaxis). The Tanimoto similarity was evaluated with ECFP4 fingerprints with counts. The transformer models trained with λ = 10 always outperforms the transformer models trained with λ = 0. The filling color surrounding solid lines represent the variance. Due to computational complexity, the similarity on GDB-12* was computed with ECFP4 fingerprints without counts. Also included in the figure is the size of the near-neighborhood retrieved from PubChem for each source compound. For HAC between 13 and 18, the neighborhood size was plotted explicitly since only a few source compounds were available in the TTD database, whereas for a HAC greater or equal than 19 the average and standard deviation are depicted.