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

arXiv: https://arxiv.org/abs/2602.22254 · HTML: https://mlsanity.com/paper/2602.22254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [The Optimal Sample Complexity of PAC Learning](https://mlsanity.com/paper/1507.00473/) (2015)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)

## Abstract (arXiv)

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.