The paper proves statistical consistency of contrastive loss to optimal ranking via an AUC criterion and derives generalization bounds O(1/m + 1/sqrt(n)) for supervised and O(1/sqrt(m) + 1/sqrt(n)) for self-supervised CRL that explain benefits of large negative sets.
arXiv preprint arXiv:1905.12600 , year=
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Statistical Consistency and Generalization of Contrastive Representation Learning
The paper proves statistical consistency of contrastive loss to optimal ranking via an AUC criterion and derives generalization bounds O(1/m + 1/sqrt(n)) for supervised and O(1/sqrt(m) + 1/sqrt(n)) for self-supervised CRL that explain benefits of large negative sets.
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A Theory on Flow Matching with Neural Networks
Establishes convergence guarantees for overparameterized 2-layer ReLU networks in flow matching, generalization bounds for the velocity-field objective, and Wasserstein guarantees for generated samples, using multi-task representation learning bounds.
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