Criticality in Dissimilar Decomposition and Undersampling of Random Datasets with Anomalies

Benchmark datasets are critical for reproducible, reliable, and discriminative evaluation of LLMs. However, recent studies reveal that many benchmark datasets are included in pretraining corpora, i.e., $\textit{contaminated}$, which diminishes their value as reliable measures of model generalization. In this paper, we argue that benchmark datasets should be $\textit{contamination-resistant}$, i.e., $\textit{unlearnable}$, but support $\textit{inference}$. To accomplish this, we first highlight the wide prevalence of benchmark dataset contamination and outline the properties of contamination-resistant datasets. Second, we highlight how the asymmetry between the inference and training pipelines in the Transformer architecture can be leveraged to support contamination-resistance. Third, we outline mathematical advancements to make these datasets interoperable across various LLM architectures. Based on the above, we call on the community to ensure the reliability of LLM benchmarking by: (i) advancing novel contamination-resistant methodologies, (ii) developing supporting methods and platforms, and (iii) adopting contamination-resistant benchmarks into existing evaluation pipelines.

This work investigates the ``small-vs-large gap'', where repeating on fewer samples can lead to compute saving during training compared to using a larger dataset. This is observed across algorithmic tasks, architectures and optimizers and cannot be explained using prior theory. We argue that the speedup comes from appropriate layer-wise growth enabled by sampling biases, which is more pronounced when the dataset size is smaller. We provide both theoretical analysis and empirical evidence from various interventions. Our results suggest that using a smaller dataset with more repetitions is not just a fallback strategy under data scarcity, but can be proactively leveraged as a favorable inductive biases for optimization, particularly in reasoning tasks.

Interpreting properties of LLM-generated data is important for understanding its utility and limitations across learning tasks. In this work, we characterize synthetic data through sample-level learnability, studying variation among LLM families and scales, alongside human-written data as a reference. We first generate synthetic datasets spanning single- and multi-label classification, labeling, and tree prediction tasks. We then derive empirical data distributions from encoder training dynamics for both machine and organic data, and estimate the robustness of these distributions across encoders. Finally, we evaluate how data selection strategies based on these learnability signals affect both data sources differently.