# Learning soft interventions in complex equilibrium systems

arXiv: https://arxiv.org/abs/2112.05729 · HTML: https://mlsanity.com/paper/2112.05729/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 10 Dec 2021.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Experimental Design in Two-Sided Platforms: An Analysis of Bias](https://mlsanity.com/paper/2002.05670/) (2020)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [Group invariance principles for causal generative models](https://mlsanity.com/paper/1705.02212/) (2017)
- [A theory of independent mechanisms for extrapolation in generative models](https://mlsanity.com/paper/2004.00184/) (2020)
- [Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layers](https://mlsanity.com/paper/2008.07303/) (2020)
- [Conditional independences and causal relations implied by sets of equations](https://mlsanity.com/paper/2007.07183/) (2020)
- [Causality and independence in perfectly adapted dynamical systems](https://mlsanity.com/paper/2101.11885/) (2021)

## Built on by (most cited first, 2 of 2)

- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Fail-Safe Adversarial Generative Imitation Learning](https://mlsanity.com/paper/2203.01696/) (2022)

## Abstract (arXiv)

Complex systems often contain feedback loops that can be described as cyclic causal models. Intervening in such systems may lead to counterintuitive effects, which cannot be inferred directly from the graph structure. After establishing a framework for differentiable soft interventions based on Lie groups, we take advantage of modern automatic differentiation techniques and their application to implicit functions in order to optimize interventions in cyclic causal models. We illustrate the use of this framework by investigating scenarios of transition to sustainable economies.