Cascading Circle Loss: Order-Preserving Contrastive Learning for Graded Legal Retrieval

This paper introduces Cascading Circle Loss (CasCL), a contrastive learning framework for legal retrieval tasks with graded relevance. CasCL combines an InfoNCE objective for positive– negative separation with a cascade of ranking boundaries that model ordered relevance levels between queries and legal clauses. The frame- work also includes a negative-aware self-paced optimization mechanism and a relevance gain weighting strategy to improve ranking quality. Experiments on legal passage retrieval bench- marks show that CasCL consistently outperforms existing methods, including InfoNCE, Circle Loss, MNRL and Margin MSE, across both bi- nary retrieval and graded ranking metrics.