@inproceedings{liu-etal-2026-quantifying,
title = "Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study",
author = "Liu, Jiaxiang and
Yuan, Chenhao and
Xu, Shuwen and
Xing, Boxuan and
Huang, Xiusheng and
Xu, Yinhao and
Liu, Hao and
Teng, Wenhao and
Liao, Xiangwen and
Cao, Pengfei and
Zhao, Jun and
Liu, Kang",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.179/",
pages = "3775--3805",
ISBN = "979-8-89176-462-0",
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 **A**tomic **T**ree **O**peration **M**odeling (**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 [GitHub](https://github.com/Lut-hub/ATOM)."
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%0 Conference Proceedings
%T Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study
%A Liu, Jiaxiang
%A Yuan, Chenhao
%A Xu, Shuwen
%A Xing, Boxuan
%A Huang, Xiusheng
%A Xu, Yinhao
%A Liu, Hao
%A Teng, Wenhao
%A Liao, Xiangwen
%A Cao, Pengfei
%A Zhao, Jun
%A Liu, Kang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F liu-etal-2026-quantifying
%X 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 **A**tomic **T**ree **O**peration **M**odeling (**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 [GitHub](https://github.com/Lut-hub/ATOM).
%U https://aclanthology.org/2026.findings-emnlp.179/
%P 3775-3805
Markdown (Informal)
[Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study](https://aclanthology.org/2026.findings-emnlp.179/) (Liu et al., Findings 2026)
ACL
- Jiaxiang Liu, Chenhao Yuan, Shuwen Xu, Boxuan Xing, Xiusheng Huang, Yinhao Xu, Hao Liu, Wenhao Teng, Xiangwen Liao, Pengfei Cao, Jun Zhao, and Kang Liu. 2026. Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 3775–3805, Budapest, Hungary. Association for Computational Linguistics.