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

Rayane Kimouche, Ahmed Touila

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 framework also includes a negative-aware self-paced optimization mechanism and a relevance gain weighting strategy to improve ranking quality. Experiments on legal passage retrieval benchmarks show that CasCL consistently outperforms existing methods, including InfoNCE, Circle Loss, MNRL and Margin MSE, across both binary retrieval and graded ranking metrics.