Learning meaningful representations of complex objects that can be seen through multiple (k≥3kgeq 3k≥3) views or modalities is a core task in machine learning. Existing methods use losses originally intended for paired views, and extend them to kkk views, either by instantiating 12k(k−1)tfrac12k(k-1)21k(k−1) loss-pairs, or by using reduced embeddings, following a one vs. average-of-resttextit{one vs. average-of-rest}one vs. average-of-rest strategy. We propose the multi-marginal matching gap (M3G), a loss that borrows tools from multi-marginal optimal transport (MM-OT) theory to…Apple Machine Learning Research