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arXiv 2602.22254cs.LGcs.AI
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从收敛时间推断因果方向:在真实因果方向上更快的训练

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

Abdulrahman Tamim

AI总结:

该研究提出CCA方法,通过优化动态中的收敛时间差异推断因果方向,实现了在真实因果方向上更快的训练,并将其扩展到因果压缩学习框架中。

摘要:

我们引入了因果计算不对称性(CCA),这是一种基于优化动态的因果方向识别原则,其中一个神经网络被训练以从X预测Y,另一个被训练以从Y预测X,而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中,ε与X独立,且f是非线性和单射的,我们建立了正式的不对称性:在反向方向,残差无论近似质量如何,都保持在输入上统计依赖,导致不可约损失底面严格更高和非分离的梯度噪声在优化动态中,因此反向模型在期望上需要严格更多梯度步骤才能达到任何固定损失阈值;因此,正向(因果)方向在更少的优化步骤中收敛。CCA在优化时间空间中运行,区别于依赖于统计独立性或分布不对称性的方法,如RESIT、IGCI和SkewScore,且对两个变量的适当标准化是有效比较收敛率的必要条件。在合成基准上,CCA在六个神经网络架构中实现了26/30次正确的因果识别,包括在正弦和指数数据生成过程中实现了30/30次正确识别。我们进一步将CCA嵌入到一个更广泛的框架中,称为因果压缩学习(CCL),该框架整合了图结构学习、因果信息压缩和策略优化,并在合成数据集上正式证明并经验验证了所有理论保证。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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