[Paper Review] What caused what? A quantitative account of actual causation using dynamical causal networks

Larissa Albantakis, William Marshall+2 more|arXiv (Cornell University)|Aug 22, 2017

Neural dynamics and brain function4 citations

TL;DR

This paper proposes a quantitative framework for identifying actual causes in discrete dynamical systems using dynamical causal networks, grounded in counterfactual reasoning, system interventions, and partitioning of state transitions. It satisfies core causal principles—realization, composition, information, integration, and exclusion—enabling precise identification and measurement of actual causes and effects across diverse causal paradoxes and real-world systems.

ABSTRACT

Actual causation is concerned with the question "what caused what?" Consider a transition between two states within a system of interacting elements, such as an artificial neural network, or a biological brain circuit. Which combination of synapses caused the neuron to fire? Which image features caused the classifier to misinterpret the picture? Even detailed knowledge of the system's causal network, its elements, their states, connectivity, and dynamics does not automatically provide a straightforward answer to the "what caused what?" question. Counterfactual accounts of actual causation based on graphical models, paired with system interventions, have demonstrated initial success in addressing specific problem cases in line with intuitive causal judgments. Here, we start from a set of basic requirements for causation (realization, composition, information, integration, and exclusion) and develop a rigorous, quantitative account of actual causation that is generally applicable to discrete dynamical systems. We present a formal framework to evaluate these causal requirements that is based on system interventions and partitions, and considers all counterfactuals of a state transition. This framework is used to provide a complete causal account of the transition by identifying and quantifying the strength of all actual causes and effects linking the two consecutive system states. Finally, we examine several exemplary cases and paradoxes of causation and show that they can be illuminated by the proposed framework for quantifying actual causation.

Motivation & Objective

• To address the fundamental question of 'what caused what?' in complex systems where causal structure is known but actual causation remains ambiguous.
• To formalize a rigorous, quantitative account of actual causation that satisfies core causal principles such as integration, exclusion, and information.
• To resolve longstanding paradoxes in causation (e.g., preemption, trumping) using counterfactual reasoning grounded in system interventions.
• To develop a generalizable method applicable to diverse systems, including neural networks and biological circuits, beyond static graphical models.

Proposed method

• Formalizing causation through a set of axiomatic requirements: realization, composition, information, integration, and exclusion.
• Using system interventions and state partitioning to evaluate all possible counterfactuals of a state transition.
• Quantifying causal strength via information-theoretic measures (e.g., effective information) to assess how much a cause contributes to an effect.
• Applying partition-based analysis to identify minimal subsets of elements that jointly account for a transition, ensuring exclusion of redundant causes.
• Constructing a complete causal account by evaluating all counterfactual transitions and selecting the most integrated, informative cause-effect pairs.
• Using dynamical causal networks to model system states and transitions, enabling application to real-world systems like neural networks and brain circuits.

Experimental results

Research questions

• RQ1 How can actual causation be formally defined and quantified in discrete dynamical systems with known causal structure?
• RQ2 How can counterfactual reasoning be systematically applied to identify actual causes without relying on intuitive judgments?
• RQ3 How can the framework resolve causal paradoxes such as preemption, trumping, and disjunctive causation?
• RQ4 What criteria ensure that identified causes are both necessary and integrated, avoiding over-attribution or redundancy?
• RQ5 How can the strength of actual causation be measured in a way that reflects both information and integration?

Key findings

• The framework successfully identifies actual causes and effects in complex transitions by evaluating all counterfactuals through system interventions and partitions.
• It quantifies causal strength using effective information, providing a numerical measure of how much a cause contributes to an effect’s realization.
• The method resolves classic causal paradoxes—such as preemption and disjunctive causation—by enforcing the exclusion and integration principles.
• The framework demonstrates consistency with intuitive causal judgments across diverse examples, including neural network dynamics and brain circuit transitions.
• It reveals that actual causation is not always reducible to single elements, but often arises from integrated, minimal subsets of interacting components.
• The approach generalizes beyond static Bayesian networks, enabling causal analysis in systems with time-varying states and dynamic interactions.