Scale Dependent Data Duplication

Abstract: Data duplication during pretraining can degrade generalization and lead to memorization, motivating aggressive deduplication pipelines. However, at web scale, it is unclear what constitutes a ``duplicate'': beyond surface-form matches, semantically equivalent documents (e.g. translations) may induce redundant training signals once models become sufficiently capable. Practically, this means that semantic duplicates operate increasingly like exact duplicates during training. We present evidence that duplication is scale-dependent in two ways. First, as model capability increases, cross-entropy loss gradients for semantically equivalent documents become more aligned. Smaller models, by contrast, produce gradients that reflect surface similarity (e.g., shared tokens) rather than semantic similarity. Second, we embedded all 192 million FineWeb-Edu-Dedup documents using EmbeddingGemma-300m. For moderate corpus sizes, the cosine similarity between nearest-neighbors follows an isotropic power law baseline. However, as corpus size grows to hundreds of billions of tokens, the nearest-neighbor similarities deviate sharply, indicating accelerated semantic collisions. Finally, controlled pretraining on data sampled with replacement from pools of finite unique documents shows that limited uniqueness yields mild degradation for small models, but rapidly increasing loss penalties for larger models, breaking naive scaling extrapolation. We derive explicit scaling laws that allow practitioners to estimate deviation from expected scaling due to limited semantic uniqueness of the pretraining corpus. Our results identify and resolve an unstudied source of scale-dependence, allowing for more accurate prediction at scale.