5 Broader impact This submission focuses on foundational and exploratory work, with application to general machine

Our experiments use data sets that are already open-sourced and cited in the references. At present, our implementation of Kruskal's algorithm is incompatible with processing very large batch sizes at train time. At inference time this is not the case, since gradients need not be back-propagated hence, any implementation of Kruskal's algorithm can be used such as the union-find implementation. Our implementation of Kruskal's is tailored to our use: we first initialize both We remark that our implementation takes the form as a single loop, with each step of the loop consisting only of matrix multiplications. This biasing ensures that any edge between points that are constrained to be in the same cluster will always be processed before unconstrained edges.