# An Analysis of the Adaptation Speed of Causal Models

arXiv: https://arxiv.org/abs/2005.09136 · HTML: https://mlsanity.com/paper/2005.09136/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2020.

## Built on by (most cited first, 9 of 9)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?](https://mlsanity.com/paper/2106.02890/) (2021)
- [CRASS: A Novel Data Set and Benchmark to Test Counterfactual Reasoning of Large Language Models](https://mlsanity.com/paper/2112.11941/) (2021)
- [Softmax is 1/2-Lipschitz: A tight bound across all ℓp norms](https://mlsanity.com/paper/2510.23012/) (2025)
- [On the Generalization and Adaption Performance of Causal Models](https://mlsanity.com/paper/2206.04620/) (2022)
- [Adaptation Speed Analysis for Fairness-aware Causal Models](https://mlsanity.com/paper/2308.16879/) (2023)
- [Prequential MDL for Causal Structure Learning with Neural Networks](https://mlsanity.com/paper/2107.05481/) (2021)
- [Convergence Rates for the MAP of an Exponential Family and Stochastic Mirror Descent -- an Open Problem](https://mlsanity.com/paper/2111.06826/) (2021)
- [Modularity Trumps Invariance for Compositional Robustness](https://mlsanity.com/paper/2306.09005/) (2023)

## Abstract (arXiv)

Consider a collection of datasets generated by unknown interventions on an unknown structural causal model G. Recently, Bengio et al. (2020) conjectured that among all candidate models, G is the fastest to adapt from one dataset to another, along with promising experiments. Indeed, intuitively G has less mechanisms to adapt, but this justification is incomplete. Our contribution is a more thorough analysis of this hypothesis. We investigate the adaptation speed of cause-effect SCMs. Using convergence rates from stochastic optimization, we justify that a relevant proxy for adaptation speed is distance in parameter space after intervention. Applying this proxy to categorical and normal cause-effect models, we show two results. When the intervention is on the cause variable, the SCM with the correct causal direction is advantaged by a large factor. When the intervention is on the effect variable, we characterize the relative adaptation speed. Surprisingly, we find situations where the anticausal model is advantaged, falsifying the initial hypothesis. Code to reproduce experiments is available at https://github.com/remilepriol/causal-adaptation-speed