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)→ 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).

As large language models (LLMs) continue to advance, there is a growing urgency to enhance the interpretability of their internal knowledge mechanisms. Consequently, many interpretation methods have emerged, aiming to unravel the knowledge mechanisms of LLMs from various perspectives. However, current interpretation methods differ in input data formats and interpreting outputs. The tools integrating these methods are only capable of supporting tasks with specific inputs, significantly constraining their practical applications. To address these challenges, we present an open-source Knowledge Mechanisms Revealer&Interpreter (Know-MRI) designed to analyze the knowledge mechanisms within LLMs systematically. Specifically, we have developed an extensible core module that can automatically match different input data with interpretation methods and consolidate the interpreting outputs. It enables users to freely choose appropriate interpretation methods based on the inputs, making it easier to comprehensively diagnose the model’s internal knowledge mechanisms from multiple perspectives. Our code is available at https://github.com/nlpkeg/Know-MRI. We also provide a demonstration video on https://youtu.be/NVWZABJ43Bs.