Enhancing molecular selectivity using Wasserstein distance based reweighing

Given a training data-set $\mathcal{S}$, and a reference data-set $\mathcal{T}$, we design a simple and efficient algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\mathcal{S}$ approaches the limiting distribution that would have resulted by training on $\mathcal{T}$. Such reweighing can be used to correct for Train-Test distribution shift, when we don't have access to the labels of $\mathcal{T}$. It can also be used to perform (soft) multi-criteria optimization on neural nets, when we have access to the labels of $\mathcal{T}$, but $\mathcal{S}$ and $\mathcal{T}$ have few common points. As a motivating application, we train a graph neural net to recognize small molecule binders to MNK2 (a MAP Kinase, responsible for cell signaling) which are non-binders to MNK1 (a very similar protein), even in the absence of training data common to both data-sets. We are able to tune the reweighing parameters so that overall change in holdout loss is negligible, but the selectivity, i.e., the fraction of top 100 MNK2 binders that are MNK1 non-binders, increases from 54\% to 95\%, as a result of our reweighing. We expect the algorithm to be applicable in other settings as well, since we prove that when the metric entropy of the input data-sets is bounded, our random sampling based greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance.