arXiv:2602.22254cs.LGcs.AI2026-02

通过训练速度差异判断因果方向,快的一边更可能是真实因果。

Causal Direction from Convergence Time: Faster Training in the True Causal Direction

  • 用双向神经网络训练,较快收敛的方向为因果方向。
  • 在真实因果方向上,优化所需梯度步数更少,理论可证。
  • 适合需要自动识别因果关系的研究者,尤其对数据生成机制未知场景有效。

我们提出因果计算不对称性(CCA),一种基于优化动态的因果方向识别方法:分别训练一个网络从X预测Y,另一个从Y预测X,收敛更快的方向被推断为因果方向。在加性噪声模型 $Y = f(X) + \ε$($\varepsilon \perp X$,$f$ 非线性且单射)下,反向模型的残差始终与输入统计相关,导致不可约损失下限更高、梯度噪声不可分离,因此反向模型期望需更多梯度步数才能达到固定损失阈值,故正向(因果)方向收敛更快。该方法基于优化时间空间,区别于依赖统计独立性或分布不对称性的方法(如RESIT、IGCI、SkewScore),要求两变量均进行适当z-score标准化以保证收敛速率可比性。在合成基准测试中,CCA在六种神经网络架构下实现26/30正确识别,其中正弦与指数数据生成过程达30/30正确。进一步,我们将CCA嵌入因果压缩学习(CCL)框架,整合图结构学习、因果信息压缩与策略优化,所有理论保证经证明并实证验证于合成数据集。

原文摘要 · Abstract (English)

We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict $Y$ from $X$ and another to predict $X$ from $Y$, and the direction that converges faster is inferred to be causal. Under the additive noise model $Y = f(X) + \varepsilon$ with $\varepsilon \perp X$ and $f$ nonlinear and injective, we establish a formal asymmetry: in the reverse direction, residuals remain statistically dependent on the input regardless of approximation quality, inducing a strictly higher irreducible loss floor and non-separable gradient noise in the optimization dynamics, so that the reverse model requires strictly more gradient steps in expectation to reach any fixed loss threshold; consequently, the forward (causal) direction converges in fewer expected optimization steps. CCA operates in optimization-time space, distinguishing it from methods such as RESIT, IGCI, and SkewScore that rely on statistical independence or distributional asymmetries, and proper z-scoring of both variables is required for valid comparison of convergence rates. On synthetic benchmarks, CCA achieves 26/30 correct causal identifications across six neural architectures, including 30/30 on sine and exponential data-generating processes. We further embed CCA into a broader framework termed Causal Compression Learning (CCL), which integrates graph structure learning, causal information compression, and policy optimization, with all theoretical guarantees formally proved and empirically validated on synthetic datasets.

因果推断优化动态神经网络

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