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Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

Synthetic data generation has become a cornerstone for advancing large language models. However, the lack of the quantitative analysis for error tolerance became a critical bottleneck. Consequently, current filtering strategies fluctuate between two extremes: they are either overly aggressive, risking the exclusion of potentially valuable samples, or overly permissive, failing to eliminate erroneous samples effectively. To bridge this gap, this paper introduces Atomic Tree Operation Modeling (ATOM), a framework that decomposes data into functional units ($f(x)\rightarrow y$). ATOM distinguishe

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