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.
10 Statistical Consistency and Generalization of Contrastive Representation Learning Gao, W
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CAPO improves LLM calibration by up to 15% while matching or exceeding GRPO accuracy through logistic AUC loss and noise masking, enabling better abstention and scaling performance.
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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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Calibration-Aware Policy Optimization for Reasoning LLMs
CAPO improves LLM calibration by up to 15% while matching or exceeding GRPO accuracy through logistic AUC loss and noise masking, enabling better abstention and scaling performance.