Contrasting Multiple Representations with the Multi-Marginal Matching Gap
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…
Learning disentangled representations from unlabelled data is a fundamental challenge in machine learning. Solving it may unlock other problems, such as generalization, interpretability, or fairness. Although remarkably challenging to solve in theory, disentanglement is often achieved in practice through prior matching. Furthermore, recent works have shown that prior matching approaches…
We give the first result for agnostically learning Single-Index Models (SIMs) with arbitrary monotone and Lipschitz activations. All prior work either held only in the realizable setting or required the activation to be known. Moreover, we only require the marginal to have bounded second moments, whereas all prior work required…