We train several neural networks and boosted decision trees to discriminate fully-hadronic boosted di-$\tau$ topologies against background QCD jets, using calorimeter and tracking information. Boosted di-$\tau$ topologies consisting of a pair of highly collimated $\tau$-leptons, arise from the decay of a highly energetic Standard Model Higgs or Z boson or from particles beyond the Standard Model. We compare the tagging performance for different neural-network models and a boosted decision tree, the latter serving as a simple benchmark machine learning model.