Drug-likeness transport no longer hinges on tuning: SBOF reaches TV 0.0141 on DrugBank while tuned Sinkhorn stays at 0.1753
Synopsis
On 5,357 structurally resolved small molecules from DrugBank 5.1.10, Schrödinger Bridge Onsager Flow drives the transport from a uniform chemical library toward a drug-likeness distribution to a total variation distance of 0.0141, against 0.1753 for a Sinkhorn baseline at its best setting across a ten-value regularization sweep. The method keeps one scalar potential per molecule updated by mirror descent instead of an all-pairs coupling matrix; its neural amortization, SBOFNet, returns a total variation distance of 0.0380 in a single forward pass with 1.6M parameters, at lower accuracy than the analytic solver.
Interpretation
Reweighting a chemical library toward drug-like regions can now update one scalar potential per molecule instead of solving the full pairwise coupling matrix, reaching a total variation distance of 0.0141 against the target on real structure-derived DrugBank data. The standard route was entropic optimal transport solved by Sinkhorn-Knopp-type algorithms; entropic regularization makes the problem tractable but blurs the target distribution, so sharp modes are hard to capture unless the regularization strength is carefully tuned. On 5,357 molecules from DrugBank 5.1.10 after PubChem SMILES enrichment and filtering to 100–900 Da, SBOF converged at iteration 87 to a total variation distance of 0.0141, KL divergence of 1.25×10⁻³ and Pearson correlation of 0.9996 in 70.1 s on a single CPU core; default Sinkhorn gave a total variation distance of 0.2571.
The advantage is not an artifact of an untuned baseline: across a sweep of ten regularization strengths from 0.005 to 5.0, the best-tuned Sinkhorn still trails clearly. At its optimal regularization strength of 0.005, Sinkhorn reaches a total variation distance of 0.1753 and a correlation of about 0.93, versus 0.0141 for SBOF, a 91.9% improvement in total variation distance. The comparison uses the same 5,357-molecule dataset and the same seven RDKit descriptors, so the gain is attributed to the algorithm's structure rather than to data or hyperparameter choice.
To score unseen molecules, SBOFNet distills the analytic potential into a network that takes the seven raw descriptors and outputs the reweighting in a single forward pass. The analytic SBOF relies on the full n×n similarity kernel, so a novel compound in a virtual screening campaign would require re-solving the entire transport problem from scratch. SBOFNet reached its best validation performance at epoch 465 with a total variation distance of 0.0380 and Pearson correlation of 0.862, trained for 500 epochs with AdamW and cosine annealing on a 90/10 train/validation split.
Perspective
The demonstrated scope is 5,357 small molecules from DrugBank 5.1.10 that matched a PubChem SMILES and fall between 100 and 900 Da, with all descriptors computed by RDKit; the analytic SBOF solves on that fixed dataset, and SBOFNet is trained and validated on a 90/10 split of the same data.
Results come from a single training seed, and the authors state that multi-seed confidence intervals are needed for absolute statistical guarantees; they also propose benchmarking against the highly optimized Python Optimal Transport library. The coverage-bias analysis shows the working set modestly under-represents high-molecular-weight compounds (450–900 Da: 19.0% versus 25.0%), while approval rates are nearly identical (22.2% versus 23.7%, p = 0.064).