Dynamic model of neural networks

Modeling of a Neural System Based on Statistical Mechanics

The minimization of a free energy is often regarded as the key principle in understanding how the brain works and how the brain structure forms. In particular, a statistical-mechanics-based neural network model is expected to allow one to interpret many aspects of the neural firing and learning processes in terms of general concepts and mechanisms in statistical physics. Nevertheless, the definition of the free energy in a neural system is usually an intricate problem without an evident solution. After the pioneering work by Hopfield, several statistical-mechanics-based models have suggested a variety of definition of the free energy or the entropy in a neural system. Among those, the Feynman machine, proposed recently, presents the free energy of a neural system defined via the Feynman path integral formulation with the explicit time variable. In this study, we first give a brief review of the previous relevant models, paying attention to the troublesome problems in them, and examine how the Feynman machine overcomes several vulnerable points in previous models and derives the outcome of the firing or the learning rule in a (biological) neural system as the extremum state in the free energy. Specifically, the model reveals that the biological learning mechanism, called spike-timing-dependent plasticity, relates to the free-energy minimization principle. Basically, computing and learning mechanisms in the Feynman machine base on the exact spike timings of neurons, such as those in a biological neural system. We discuss the consequence of the adoption of an explicit time variable in modeling a neural system and the application of the free-energy minimization principle to understanding the phenomena in the brain.

Modelling studies on the computational function of fast temporal structure in cortical circuit activity

The interplay between modelling and experimental studies can support the exploration of the function of neuronal circuits in the cortex. We exemplify such an approach with a study on the role of spike timing and gamma-oscillations in associative memory in strongly connected circuits of cortical neurones. It is demonstrated how associative memory studies on different levels of abstraction can specify the functionality to be expected in real cortical neuronal circuits. In our model overlapping random configurations of sparse cell populations correspond to memory items that are stored by simple Hebbian coincidence learning. This associative memory task will be implemented with biophysically well tested compartmental neurones developed by Pinsky and Rinzel . We ran simulation experiments to study memory recall in two network architectures: one interconnected pool of cells, and two reciprocally connected pools. When recalling a memory by stimulating a spatially overlapping set of cells, the completed pattern is coded by an event of synchronized single spikes occurring after 25-60 ms. These fast associations are performed even at a memory load corresponding to the memory capacity of optimally tuned formal associative networks (>0.1 bit/synapse). With tonic stimulation or feedback loops in the network the neurones fire periodically in the gamma-frequency range (20-80 Hz). With fast changing inputs memory recall can be switched between items within a single gamma cycle. Thus, oscillation is not a primary coding feature necessary for associative memory. However, it accompanies reverberatory feedback providing an improved iterative memory recall completed after a few gamma cycles (60-260 ms). In the bidirectional architecture reverberations do not express in a rigid phase locking between the pools. For small stimulation sets bursting occurred in these cells acting as a supportive mechanism for associative memory.

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train.