  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.
