Causal Direction from Convergence Time: Faster Training in the True Causal Direction
This provides a new method for causal inference researchers, though it appears incremental as it builds on existing optimization dynamics.
The paper tackles the problem of identifying causal direction by proposing Causal Computational Asymmetry (CCA), which uses faster neural network training convergence as an indicator, and shows it achieves 26/30 correct identifications on synthetic benchmarks.
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.