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. In the majority of conditions we test, CDD performs at chance level even when the data is verifiably contaminated and detectable by simpler methods. We show that probability-based methods, specifically perplexity and Min-k\% Prob, outperform CDD in all conditions where any method exceeds chance, suggesting that CDD's peakedness-based approach is insufficient for contamination detection in small language models. Our code is available at https://github.com/Sela-Omer/Contamination-Detection-Small-LM