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We assume that complex tasks are executed by goingthrough a series of inner mental states, each representingan actively maintained disposition to behavior. Each statecontains task relevant information about past events andinternal cognitive processes. For example, in complextasks the same sensory stimulus might require differentmotor responses depending on the context. More gener-ally, decisions are affected by a large number of factorssuch as motivations, emotions and intentions, which areall assumed to be encoded in the inner mental state. Everytask relevant event induces a transition from one mentalstate to another. This implies that mental states arenumerous and the event driven transitions between themare highly organized.We constructed tasks in which the schemes of mentalstates and event driven transitions are hierarchicallyorganized and scalable in complexity. We then built amodel of a neural network that performs these tasks. Weassumed that mental states are represented by stableattractors of neural dynamics, with external events steer-ing the activity from one state to another. The structure ofmental states and event driven transitions is encoded inthe synaptic couplings between neurons, and it containsthe instructions to react to the events occurring in theexternal world.We show that there is a wide class of hierarchically organ-ized schemes of mental states and event driven transitionsthat produce neural activity with long-range temporal cor-relations. In particular, the autocorrelation function of theneural activity decays as a power-law on a time intervalthat increases linearly with the number of mental states.The power-law behavior is entirely due to the hierarchicalstructure of the scheme of mental states as the events arealways assumed to be delta correlated. Power-law autocor-relations are widely observed in recorded activity inbehaving animals [1].Highly variable neural activity might also be an expres-sion of the dynamics of a neural network implementing acomplex scheme of mental states and event driven transi-tions. Experiments show that there are rapid changes inthe recorded neural activity that can be interpreted as sud-den transitions from one state to another [2,3]. Thesetransitions can occur also in the interval between two taskrelevant events, indicating that there might be multipleprocessing stages during the perception of a sensory stim-ulus. Such stages would correspond to different mentalstates and the transitions would be generated either inter-nally, by other cognitive processes, or externally, by eventsthat are not under control in the experimental protocol.The fluctuations in the neural activity caused by these fre-quent transitions have a 1/

Power-law autocorrelation of neural activity in models of mental states that are hierarchically organized