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Towards a Grounded Theory of Causation for Embodied AI
Taco Cohen
TL;DR
Autonomous causal modelling lacks clear guidance for choosing variables and deciding which agent behaviours count as interventions, although those choices are needed for agents to learn through interaction. The paper represents actions as transformations of state space, defines when they set invariant mechanisms surgically, and relates abstract models to underlying dynamics. It concludes that this reconstructs SCM theory while grounding and extending the account of interventions as physical processes.
Problem
Existing causal frameworks leave variable representation and the status of policy-driven or physical state transformations as interventions unclear, while autonomous agents lack the human expertise used to define variables and interventions.
Source: §1 · p. 1Method
The paper models policies as state-space transformations, relates abstract models to system dynamics, and characterizes variables, invariant mechanisms, and surgical interventions.
Source: §1 · p. 1, §3.2 · p. 5Results
The framework reconstructs SCM theory while also describing non-surgical actions, graph changes, and properties of actions such as non-commutativity.
Source: §5 · p. 6Takeaways & Limitations
Treating interventions as physically possible state-space processes gives causal representation and intervention skill learning a concrete grounding in agent behaviour.
Source: §1 · p. 1, §5 · p. 6The paper does not address partial observability or beliefs, and leaves open which virtual actions should be admitted.
Source: §2.3 · p. 3
Abstract
from arXiv · showhide
There exist well-developed frameworks for causal modelling, but these require rather a lot of human domain expertise to define causal variables and perform interventions. In order to enable autonomous agents to learn abstract causal models through interactive experience, the existing theoretical foundations need to be extended and clarified. Existing frameworks give no guidance regarding variable choice / representation, and more importantly, give no indication as to which behaviour policies or physical transformations of state space shall count as interventions. The framework sketched in this paper describes actions as transformations of state space, for instance induced by an agent running a policy. This makes it possible to describe in a uniform way both transformations of the micro-state space and abstract models thereof, and say when the latter is veridical / grounded / natural. We then introduce (causal) variables, define a mechanism as an invariant predictor, and say when an action can be viewed as a ``surgical intervention'', thus bringing the objective of causal representation \& intervention skill learning into clearer focus.
1 INTRODUCTION
Autonomous agents lack the human concepts and skills that make causal variables and interventions clear in scientific applications. The paper proposes modelling actions as state-space transformations and asks when they count as surgical interventions that set causal mechanisms.
1 INTRODUCTION
- Causal modelling for autonomous agents requires learning both causal representations and intervention skills that can set variable mechanisms.The desired interventions would be surgical enough to support simple SCM-like causal reasoning.Source: §1 · p. 1
- Low-level MDP actions such as robot motor commands do not by themselves provide meaningful interventions, leaving open how policies set mechanisms surgically.The paper identifies variable choice, mechanism, and surgical intervention as foundational questions.Source: §1 · p. 1
- The framework models policies as transformations of a state space and models subsequent outcomes through a process map.It treats the agent’s model of actions and process as an abstraction of underlying dynamics, with uncertainty incorporable through noise distributions.Source: §1 · p. 1
- The paper introduces causal variables and conditions under which actions act as surgical interventions, and shows that its framework can encode any SCM.It illustrates the ideas with a robot arm and dominoes, then discusses implications for causal representation and intervention-skill learning.Source: §1 · p. 1
2 MODELS OF ACTIONS & OUTCOMES
Actions are represented as maps on system states, followed by a process that produces outcomes; composing actions yields counterfactual outcome maps. The section illustrates this setup with robot-manipulated dominoes, defines mathematical relations between system and abstract models, and discusses uncertainty and virtual actions.
2 MODELS OF ACTIONS & OUTCOMES
- A policy run for a fixed duration or until termination induces a state-to-state action map, and subsequent process maps yield outcomes that depend on the starting state.Composite actions use function composition; the setup assumes no intervening observation or action during the outcome process.Source: §2 · p. 2
2.1 RUNNING EXAMPLE: ROBO-DOMINOES
- The robot-domino example uses skills to configure dominoes and designate a push before the process pushes the chosen domino and records the resulting state.The setup includes actions such as placing barriers, moving dominoes, and choosing a push.Source: §2.1 · p. 2
2.2 NATURAL MAPS BETWEEN MODELS
- A veridical abstraction relates system and model states and outcomes by maps that make the action and process diagrams commute.The model need not represent the full system state; naturality requires action and prediction paths to agree.Source: §2.2 · p. 3
- Naturality gives a function-level account of veridicality and preserves the compositional structure of interventions.The paper also relates naturality to equivariance in geometric deep learning.Source: §2.2 · p. 3
2.3 UNCERTAINTY AND VIRTUAL ACTIONS
- The framework assumes the model state contains enough information to determine outcomes and leaves partial observability and beliefs outside its scope.It also allows virtual actions without an implementing policy, while noting that which virtual actions to admit is unresolved and physical possibility may matter.Source: §2.3 · p. 3
3 CAUSAL VARIABLES, MECHANISMS & INTERVENTIONS
The section formalizes causal variables as components of outcomes, then develops determination and invariance as foundations for identifying mechanisms and surgical interventions. It also shows how SCMs can be represented in this framework and discusses when that representation is useful.
3 CAUSAL VARIABLES, MECHANISMS & INTERVENTIONS
- Actions can restrict the possible outcomes of a process because precomposing its map with an action cannot increase its image.The outcome variables are projections of the process outcome, and their possible joint assignments need not all be attainable.Source: §3 · p. 4
- A variable representation can include joint assignments that never occur, so causal representation learning should not assume every combination or interpolation is valid.The set of possible outcomes carries information about system constraints.Source: §3 · p. 4
3.1 DETERMINATION & EFFECTIVE ACTIONS
- Determination means one outcome-variable set predicts another through a map, but determination alone does not establish a mechanism.It is invariant to actions performed before the determining action, but need not remain invariant to actions performed afterward; it may also hold only in a context.Source: §3.1 · pp. 4–5
3.2 INVARIANT MECHANISMS
- A surgical intervention invalidates exactly one active mechanism and installs a new invariant mechanism for its target variable.An effective, or atomic, intervention installs a constant mechanism; other interventions can install a function.Source: §3.2 · p. 5
3.3 STRUCTURAL CAUSAL MODELS
- The framework encodes SCMs by representing exogenous variables and mechanisms in the state, then defining outcomes through the SCM’s potential responses.Interventions on different variables commute, while interventions on the same variable overwrite one another.Source: §3.3 · p. 6
- The encoding is most useful when variables and interventions are learned through interaction or when a single DAG cannot describe the system’s actions.The map-based framework also supports defining veridicality and model abstraction through natural transformations.Source: §3.3 · p. 6
4 DISCUSSION & RELATED WORK
The discussion places the framework alongside work on causal representation learning and variable choice, and identifies a gap in relating microscopic processes to interventions in causal models.
4 DISCUSSION & RELATED WORK
- Many causal representation learning approaches focus on learning representations from data and do not consider intervention policies.The discussion situates this gap alongside work including Schölkopf et al. [2021] and several other cited approaches.Source: §4 · p. 6
- Prior work had not established when a microscopic process can be described as an atomic or soft intervention in a causal model.The paper frames this as a fundamental issue for causal representation and intervention skill learning.Source: §4 · p. 6
- The framework treats interventions as composable processes and uses bare sets and maps rather than differential equations.The discussion contrasts this focus with work on causal models emerging from systems of differential equations.Source: §4 · p. 6
5 CONCLUSION
The conclusion presents interventions as physically possible state-space transformations and mechanisms as invariant predictors, grounding a reconstruction of SCM theory in behavior.
5 CONCLUSION
- The framework defines an intervention as a physically possible state-space transformation and answers when it surgically sets an invariant mechanism for a variable.It reconstructs SCM theory while allowing actions that are not surgical, can drastically change the graph, and may not commute.Source: §5 · p. 6