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

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.Comment: 43 pages, 16 figures, supplementary discussion, supplementary methods, supplementary proof

When is an action caused from within? Quantifying the causal chain leading to actions in simulated agents

An agent's actions can be influenced by external factors through the inputs it receives from the environment, as well as internal factors, such as memories or intrinsic preferences. The extent to which an agent's actions are "caused from within", as opposed to being externally driven, should depend on its sensor capacity as well as environmental demands for memory and context-dependent behavior. Here, we test this hypothesis using simulated agents ("animats"), equipped with small adaptive Markov Brains (MB) that evolve to solve a perceptual-categorization task under conditions varied with regards to the agents' sensor capacity and task difficulty. Using a novel formalism developed to identify and quantify the actual causes of occurrences ("what caused what?") in complex networks, we evaluate the direct causes of the animats' actions. In addition, we extend this framework to trace the causal chain ("causes of causes") leading to an animat's actions back in time, and compare the obtained spatio-temporal causal history across task conditions. We found that measures quantifying the extent to which an animat's actions are caused by internal factors (as opposed to being driven by the environment through its sensors) varied consistently with defining aspects of the task conditions they evolved to thrive in.Comment: Submitted and accepted to Alife 2019 conference. Revised version: edits include adding more references to relevant work and clarifying minor points in response to reviewer

The Role of Conditional Independence in the Evolution of Intelligent Systems

Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked systems, both digital and biological, each component receives inputs, performs a simple computation, and creates an output. When these components have multiple outputs, we intuitively assume that the outputs are causally dependent on the inputs but are themselves independent of each other given the state of their shared input. However, this intuition can be violated for components with probabilistic logic, as these typically cannot be decomposed into separate logic gates with one output each. This violation of conditional independence on the past system state is equivalent to instantaneous interaction --- the idea is that some information between the outputs is not coming from the inputs and thus must have been created instantaneously. Here we compare evolved artificial neural systems with and without instantaneous interaction across several task environments. We show that systems without instantaneous interactions evolve faster, to higher final levels of performance, and require fewer logic components to create a densely connected cognitive machinery.Comment: Original Abstract submitted to the GECCO conference 2017 Berli

Black-boxing and cause-effect power

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by employing a principled, well-defined measure of intrinsic cause-effect power - integrated information ({\Phi}), and showing that, according to this measure, it is possible for a macro level to "beat" the micro level. Simple systems were evaluated for {\Phi} across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro updates. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal micro elements that support their input-output function. We show how black-box elements can have more common inputs and outputs than the corresponding micro elements, revealing the emergence of high-order mechanisms and joint constraints that are not apparent at the micro level. As a consequence, a macro, black-box system can have higher {\Phi} than its micro constituents by having more mechanisms (higher composition) that are more interconnected (higher integration). We also show that, for a given micro system, one can identify local maxima of {\Phi} across several spatiotemporal scales. The framework is demonstrated on a simple biological system, the Boolean network model of the fission-yeast cell-cycle, for which we identify stable local maxima during the course of its simulated biological function. These local maxima correspond to macro levels of organization at which emergent cause-effect properties of physical systems come into focus, and provide a natural vantage point for scientific inquiries.Comment: 45 pages (32 main text, 13 supplementary), 14 figures (9 main text, 5 supplementary

PyPhi: A toolbox for integrated information theory

Integrated information theory provides a mathematical framework to fully characterize the cause-effect structure of a physical system. Here, we introduce PyPhi, a Python software package that implements this framework for causal analysis and unfolds the full cause-effect structure of discrete dynamical systems of binary elements. The software allows users to easily study these structures, serves as an up-to-date reference implementation of the formalisms of integrated information theory, and has been applied in research on complexity, emergence, and certain biological questions. We first provide an overview of the main algorithm and demonstrate PyPhi's functionality in the course of analyzing an example system, and then describe details of the algorithm's design and implementation. PyPhi can be installed with Python's package manager via the command 'pip install pyphi' on Linux and macOS systems equipped with Python 3.4 or higher. PyPhi is open-source and licensed under the GPLv3; the source code is hosted on GitHub at https://github.com/wmayner/pyphi . Comprehensive and continually-updated documentation is available at https://pyphi.readthedocs.io/ . The pyphi-users mailing list can be joined at https://groups.google.com/forum/#!forum/pyphi-users . A web-based graphical interface to the software is available at http://integratedinformationtheory.org/calculate.html .Comment: 22 pages, 4 figures, 6 pages of appendices. Supporting information "S1 Calculating Phi" can be found in the ancillary file

Only what exists can cause: An intrinsic view of free will

This essay addresses the implications of integrated information theory (IIT) for free will. IIT is a theory of what consciousness is and what it takes to have it. According to IIT, the presence of consciousness is accounted for by a maximum of cause-effect power in the brain. Moreover, the way specific experiences feel is accounted for by how that cause-effect power is structured. If IIT is right, we do have free will in the fundamental sense: we have true alternatives, we make true decisions, and we - not our neurons or atoms - are the true cause of our willed actions and bear true responsibility for them. IIT's argument for true free will hinges on the proper understanding of consciousness as true existence, as captured by its intrinsic powers ontology: what truly exists, in physical terms, are intrinsic entities, and only what truly exists can cause.Comment: 26 pages, 12 figure