Reasoning in large language models has long been a central research focus, and recent studies employing reinforcement learning (RL) have introduced diverse methods that yield substantial performance gains with minimal or even no external supervision. Surprisingly, some studies even suggest that random or incorrect reward signals can enhance performance. However, these breakthroughs are predominantly observed for the mathematically strong Qwen2.5 series on benchmarks such as MATH-500, AMC, and AIME, and seldom transfer to models like Llama, which warrants a more in-depth investigation. In this work, our empirical analysis reveals that pre-training on massive web-scale corpora leaves Qwen2.5 susceptible to data contamination in widely used benchmarks. Consequently, conclusions derived from contaminated benchmarks on Qwen2.5 series may be unreliable. To obtain trustworthy evaluation results, we introduce a generator that creates fully clean arithmetic problems of arbitrary length and difficulty, dubbed RandomCalculation. Using this leakage-free dataset, we show that only accurate reward signals yield steady improvements that surpass the base model’s performance boundary in mathematical reasoning, whereas random or incorrect rewards do not. Moreover, we conduct more fine-grained analyses to elucidate the factors underlying the different performance observed on the MATH-500 and RandomCalculation benchmarks. Consequently, we recommend that future studies evaluate models on uncontaminated benchmarks and, when feasible, test various model series to ensure trustworthy conclusions about RL and related methods.

Data diversity is crucial for the instruction tuning of large language models. Existing studies have explored various diversity-aware data selection methods to construct high-quality datasets and enhance model performance. However, the fundamental problem of precisely defining and measuring data diversity remains underexplored, limiting clear guidance for data engineering. To address this, we systematically analyze 11 existing diversity measurement methods by evaluating their correlation with model performance through extensive fine-tuning experiments. Our results indicate that a reliable diversity measure should properly account for both inter-sample differences and the information density in the sample space. Building on this, we propose NovelSum, a new diversity metric based on sample-level “novelty.” Experiments on both simulated and real-world data show that NovelSum accurately captures diversity variations and achieves a 0.97 correlation with instruction-tuned model performance, highlighting its value in guiding data engineering practices. With NovelSum as an optimization objective, we further develop a greedy, diversity-oriented data selection strategy that outperforms existing approaches, validating both the effectiveness and practical significance of our metric.