用临界渗流模型生成有层次结构的合成数据，用于更真实地测试可解释性方法。
Critical Percolation as a Synthetic Data Model for Interpretability
- 基于临界渗流构造分形稀疏数据，具自相似性和幂律分布。
- 能线性采样随机树与层级潜变量，支持任意规模数据生成。
- 结果表明神经网络激活可线性解码真实潜变量，适合可解释性研究。
神经网络学习的特征反映了自然数据的分层多尺度结构。现有用于评估可解释性方法的合成数据集通常缺乏这种结构，限制了其作为真实简化模型的价值。为此，我们引入一类合成数据集，其由定义在高维数据空间中临界均场渗流簇上的分层函数构成。渗流数据表现为稀疏、低维的分形簇，具有幂律大小分布。潜变量建模分类层级，决定每个数据点的目标值。该数据模型解析可解，已知临界指数固定其性质，无需超参数调优。我们利用渗流簇、随机树与加性凝聚之间的映射关系，提出近似线性时间算法，可联合采样随机树及其分层潜变量分解，实现任意规模的数据生成。通过探测实验发现，模型的真实潜变量可从神经网络激活中线性解码。稀疏性、自相似性、幂律统计与解析可解性共同使临界渗流成为可解释性研究的原理性测试平台。
原文摘要 · Abstract (English)
Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. To close this gap, we introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. The data model is analytically tractable with known critical exponents that fix its properties without requiring hyperparameter tuning. We leverage a mapping between percolation clusters, random trees, and additive coalescence to propose an almost linear-time algorithm to jointly sample a random tree and its hierarchical latent decomposition, enabling data generation at arbitrary scale. Using probing experiments, we find that the model's ground-truth latent variables can be linearly decoded from neural network activations. Together, sparsity, self-similarity, power-law statistics, and analytical tractability make critical percolation a principled testbed for interpretability research.
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