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

TL;DR

This paper introduces Causal Computational Asymmetry (CCA), a novel method for causal inference based on the faster convergence of neural networks trained to predict in the causal direction, supported by theoretical and empirical validation.

Contribution

The paper proposes CCA, a new optimization-based causal inference method that distinguishes causal direction by convergence speed, with formal theoretical analysis and strong empirical results.

Findings

CCA correctly identifies causal direction in 26/30 synthetic cases

CCA converges faster in the true causal direction across multiple neural architectures

Theoretical analysis shows residual dependence causes higher irreducible loss in reverse direction

Abstract

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.