Large language models (LLMs) frequently generate hallucinations, which are unsupported by a source document. To avoid costly LLM-as-evaluator pipelines and the heavy annotation demands of existing classifiers, we propose CPIL (Cross Paraphrastic Invariance Learning), a two-stage Siamese framework that maximizes the utility of existing labeled data. Concretely, CPIL constructs informative training pairs by: (i) generating paraphrastic views of each document-claim example as positives, and explicitly aligning their representations to enforce invariance to surface form; and (ii) mining same-document, opposite-label pairs as hard negatives to sharpen document-sensitive decision boundaries. Then CPIL conduct a two-stage model training: Stage 1 performs contrastive pretraining to learn a paraphrase-invariant, grounding-aware embedding space; and Stage 2 attaches a lightweight classifier for binary groundedness. On the LLM-AggreFact benchmark (11 tasks), CPIL surpasses strong baselines concerning F1 scores with only ~1% labeled data, showing its prediction superiority and label efficiency.