Integrated information and dimensionality in continuous attractor dynamics

There has been increasing interest in the integrated information theory (IIT) of consciousness, which hypothesizes that consciousness is integrated information within neuronal dynamics. However, the current formulation of IIT poses both practical and theoretical problems when empirically testing the theory by computing integrated information from neuronal signals. For example, measuring integrated information requires observing all the elements in a considered system at the same time, but this is practically very difficult. Here, we propose that some aspects of these problems are resolved by considering the topological dimensionality of shared attractor dynamics as an indicator of integrated information in continuous attractor dynamics. In this formulation, the effects of unobserved nodes on the attractor dynamics can be reconstructed using a technique called delay embedding, which allows us to identify the dimensionality of an embedded attractor from partial observations. We propose that the topological dimensionality represents a critical property of integrated information, as it is invariant to general coordinate transformations. We illustrate this new framework with simple examples and discuss how it fits with recent findings based on neural recordings from awake and anesthetized animals. This topological approach extends the existing notions of IIT to continuous dynamical systems and offers a much-needed framework for testing the theory with experimental data by substantially relaxing the conditions required for evaluating integrated information in real neural systems.