No Memorization, No Detection: Output Distribution-Based Contamination Detection in Small Language Models

CDD, or Contamination Detection via output Distribution, identifies data contamination by measuring the peakedness of a model's sampled outputs. We study the conditions under which this approach succeeds and fails on small language models ranging from 70M to 410M parameters. Using controlled contamination experiments on GSM8K, HumanEval, and MATH, we find that CDD's effectiveness depends critically on whether fine-tuning produces verbatim memorization. With low-rank adaptation, models can learn from contaminated data without memorizing it, and CDD performs at chance level even when the data is verifiably contaminated. Only when fine-tuning capacity is sufficient to induce memorization does CDD recover strong detection accuracy. Our results characterize a memorization threshold that governs detectability and highlight a practical consideration: parameter-efficient fine-tuning can produce contamination that output-distribution methods do not detect. Our code is available at https://github.com/Sela-Omer/Contamination-Detection-Small-LM