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This paper introduces a unified geometric framework showing that weighted InfoNCE objectives can be interpreted as Distance Geometry Problems, providing exact characterizations of optimal embeddings for supervised and weakly supervised contrastive learning methods and revealing when such embeddings are geometrically realizable, degenerate, or inconsistent.
This paper introduces UniSD, a unified self-distillation framework for adapting large language models that integrates mechanisms for supervision reliability, representation alignment, and training stability. Experimental results show that UniSD improves performance over base models and existing baselines across multiple benchmarks.