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This research addresses a critical bottleneck in synthetic data generation for large language models by introducing ATOM, a framework that distinguishes between benign input variations and fatal functional errors. The study demonstrates that model robustness relies more heavily on operator diversity than on operand precision, offering a new strategy to optimize filtering without discarding valuable samples. By shifting focus from aggressive precision checks to preserving functional integrity, this work provides a practical pathway to improve data quality in AI training pipelines.
Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study
arXiv:2608.29144v1 Announce Type: new Abstract: 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 distinguishes benign Operand $x$ perturbations from fatal Operator $f$ perturbations. The former are needlessly discarded by aggressive filtering, while the latter slip through permissive filtering. Our experiments reveal a double dissociation: models are robust to operand perturbations but collapse under operator perturbations. By prioritizing operator over aggressive operand precision, our ATOM-synthesized data outperforms rigorous baselines (e.g., +3.1% gain over LIMA), suggesting that operator diversity matters more than operand precision. Our code is available at https://github.com/Lut-hub/ATOM.
Title:Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study
Abstract: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 distinguishes benign Operand $x$ perturbations from fatal Operator $f$ perturbations. The former are needlessly discarded by aggressive filtering, while the latter slip through permissive filtering. Our experiments reveal a double dissociation: models are robust to operand perturbations but collapse under operator perturbations. By prioritizing operator over aggressive operand precision, our ATOM-synthesized data outperforms rigorous baselines (e.g., +3.1% gain over LIMA), suggesting that operator diversity matters more than operand precision. Our code is available at this https URL.
Computation and Language (cs.CL)
arXiv:2608.29144 [cs.CL]
(or arXiv:2608.29144v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2608.29144 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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