Neural network (NN)-based nonlinear causal discovery methods recover DAG structure but leave each causal mechanism as a black box. Waxman et al. argued that extracting causal mechanisms from NN weights is ill-posed. We propose EML-CD, a framework that integrates the EML operator (capable of composing elementary functions from a single binary operator) into causal structure learning, with interpretable mechanism recovery as the primary objective. EML-CD represents each edge mechanism as a gated EML binary tree and automatically discovers closed-form causal equations. Analytical Jacobians can be directly computed from the output equations, enabling quantitative understanding of causal effects. On real data (Sachs protein signaling, d=11), EML-CD achieves SHD=11.2 +/- 0.4 (5-seed mean; baselines are single deterministic runs), on par with PC/GES within seed variance and below CAM, while attaching closed-form equations to each detected edge (precision 0.756, recall 0.365). In a controlled bivariate test with known mechanisms, EML-CD recovers 10 of 11 elementary function families faithfully (held-out shape correlation >= 0.96; only high-frequency sine is partial). On a symbolic synthetic benchmark, EML-CD attains a substantially lower and more stable held-out mechanism f-MSE than a fixed SINDy dictionary (mean 3.67 vs. 7644, the latter inflated by catastrophic extrapolation on one seed), although its structure recovery (SHD 14.0) only matches the dictionary and stays below specialized optimizers; on the Causal Chambers light-tunnel subset, a depth-2 model improves F1 over linear OLS-BIC (0.444 vs. 0.273).

翻译：基于神经网络的非线性因果发现方法虽能恢复有向无环图结构，但将每个因果机制视为黑箱。Waxman等人指出，从神经网络权重中提取因果机制是不适定问题。我们提出EML-CD框架，将EML算子（能够通过单一二元算符组合初等函数）集成到因果结构学习中，以可解释的机制恢复为主要目标。EML-CD将每条边机制表示为带门控的EML二叉树，并自动发现闭式因果方程。通过输出方程可直接解析计算雅可比矩阵，从而实现对因果效应的定量理解。在真实数据（Sachs蛋白信号网络，d=11）上，EML-CD在种子方差范围内达到与PC/GES相当的SHD=11.2±0.4（5次种子均值；基线为单次确定性运行），低于CAM，同时为每条检测到的边附加闭式方程（精确率0.756，召回率0.365）。在已知机制的控制双变量测试中，EML-CD忠实恢复了11个初等函数族中的10个（留出形状相关性≥0.96；仅高频正弦函数部分恢复）。在符号合成基准测试中，EML-CD的留出机制f-MSE显著低于固定SINDy字典（均值3.67对比7644，后者因单个种子的灾难性外推而膨胀），尽管其结构恢复能力（SHD=14.0）仅与字典持平且低于专用优化器；在Causal Chambers光隧道子集上，深度为2的模型相比线性OLS-BIC提升了F1分数（0.444对比0.273）。