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 based on system interventions and partitions, which 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.
Highlights
The nature of cause and effect has been much debated in both philosophy and the sciences.To date, there is no single widely-accepted account of causation, and the various sciences focus on different aspects of the issue [1]
In the following we aim to translate the information theory (IIT) account of potential causation into a principled, quantitative framework for actual causation, which allows for the evaluation of all actual causes and effects within a state transition of a dynamical system of interacting elements, such as a biological or artificial neural network
Most causal networks analyzed in the following are, deterministic, corresponding to prominent test cases of counterfactual accounts of actual causation (e.g., [8,11,19,20,21,45])
Summary
The nature of cause and effect has been much debated in both philosophy and the sciences.To date, there is no single widely-accepted account of causation, and the various sciences focus on different aspects of the issue [1]. No formal notion of causation seems to even be required for describing the dynamical evolution of a system by a set of mathematical equations. The notion of causation is reduced to the basic requirement that causes must precede and be able to influence their effects—no further constraints are imposed with regard to “what caused what”. A detailed record of “what happened” prior to a particular occurrence rarely provides a satisfactory explanation for why it occurred in causal, mechanistic terms (see Theory 2.2 for a formal definition of the term “occurrence” as a set of random variables in a particular state at a particular time). Understanding why AlphaGo chose a particular move is a non-trivial problem [3], even though all its network parameters and its state evolution can be recorded in detail. Identifying “what caused what” becomes difficult in complex systems with a distributed, recurrent
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