A new framework proposes that the topological dimensionality of shared attractor dynamics can serve as an indicator of integrated information in continuous dynamical systems, addressing practical and theoretical problems in testing integrated information theory (IIT) of consciousness with neuronal signals. The approach uses delay embedding to reconstruct the effects of unobserved nodes on attractor dynamics, allowing identification of the embedded attractor's dimensionality from partial observations. This topological measure is invariant to general coordinate transformations, extending IIT to continuous systems and relaxing conditions needed for evaluating integrated information in real neural data.
The integrated information theory (IIT) of consciousness proposes that consciousness corresponds to integrated information within neuronal dynamics, but testing this theory empirically is difficult because it requires observing all elements of a neural system simultaneously. This paper suggests that the topological dimensionality of shared attractor dynamics can serve as an indicator of integrated information in continuous attractor dynamics. Using delay embedding, effects of unobserved nodes can be reconstructed from partial observations, allowing identification of the embedded attractor's dimensionality. The topological dimensionality is invariant to coordinate transformations and thus represents a critical property of integrated information. This approach extends IIT to continuous dynamical systems and relaxes the conditions needed to evaluate integrated information in real neural systems, offering a framework for testing the theory with experimental data.