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Actual causation is concerned with the question "what caused what?" Considera transition between two states within a system of interacting elements, suchas an artificial neural network, or a biological brain circuit. Whichcombination of synapses caused the neuron to fire? Which image features causedthe classifier to misinterpret the picture? Even detailed knowledge of thesystem's causal network, its elements, their states, connectivity, and dynamicsdoes not automatically provide a straightforward answer to the "what causedwhat?" question. Counterfactual accounts of actual causation based on graphicalmodels, paired with system interventions, have demonstrated initial success inaddressing 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 todiscrete dynamical systems. We present a formal framework to evaluate thesecausal requirements that is based on system interventions and partitions, andconsiders all counterfactuals of a state transition. This framework is used toprovide a complete causal account of the transition by identifying andquantifying the strength of all actual causes and effects linking the twoconsecutive system states. Finally, we examine several exemplary cases andparadoxes of causation and show that they can be illuminated by the proposedframework for quantifying actual causation.

What caused what? A quantitative account of actual causation using dynamical causal networks