Study On Correlated Firing In Feedback Spiking Neural Networks For Stimulus Coding

One basic research topic for analyzing biological neural system is how to make connections between information processing results of neurons and the sensory stimuli. During the tasks, correlated activity of neural population has made great contribution to the information integration and analysis. The modes of correlated firing are considered to be associated with coding, recognition, computation, and memory in neural systems. The architecture of networks based on synaptic connections has important influence on the correlated firing of the neurons. Therefore, it is beneficial to research the correlated activity of neurons in particular networks, such as the networks for stimulus coding, for understanding the mechanism underlying neural information processing.As shown by the studies on neurophysiology, the correlated activity can be induced by common external stimuli and selective enhancement of part of synaptic connections between neurons. In addition, feedback involved in composing signaling pathway is an important factor in inducing correlated activity. Researches in experiments of brain slices and theory reveal that the inhibitory feedback can assist in phase-locking. Whereas, the effect of inhibitory feedback on correlated activity in network models for stimulus coding is poorly understood and the mechanisms underlying correlated firing in feedback spiking neural networks for stimulus coding need further study. Based on integrate-and-fire neuron model, the correlated activity of excitatory neurons and its relationship to inhibitory feedback are studied in feedback spiking neural network for stimulus coding. Associated with the research on the correlation of the networks with heterogeneity and synaptic plasticity, simulation results reveal the functions of inhibitory feedback in dynamic neuronal population coding. The main research achievements include the following four contents:(1) The power of synchronized oscillations in the network is found to increase with the enhancement of inhibitory feedback, while the frequency of synchronized oscillations remains the same. The correlation of the excitatory neurons in millisecond time scale is described by power spectral density. The feedback spiking neural network for stimulus coding is proved to oscillate in gamma frequency. Numerical simulations show that the power of synchronized oscillations is proportional to the strength of feedback, while the frequency of synchronized oscillations remains the same. Therefore, the correlated activity of neuronal population can be modulated by feedback when the neural system encodes external stimulus with certain frequency.(2) The correlation coefficient of network is a non-monotonic function of the strength of the feedback gain. The correlation coefficient of the network in hundreds of milliseconds time scale is estimated by the cross-correlogram of the spike trains. When the inhibitory feedback is weak, the network correlation coefficient is decreased with increasing the strength of the inhibitory feedback. However, the network correlation coefficient rises after the feedback strength exceeds a certain value. Afterwards, a stable and relatively high level of correlation coefficient is maintained with further increases in feedback strength. Considering the correlated firing activity in hundreds of milliseconds time scale, the results of computer simulations show that the inhibitory feedback could not always increase the correlation coefficient of the network.(3) The mechanism underlying the non-monotonic relationship between the network correlation coefficient and the inhibitory feedback strength is studied. Two opposing effects of the inhibitory feedback on the correlated activity in the network can explain the non-monotonic relationship. On one hand, feedback inhibits firing activity of the excitatory neurons, leading to decreasing of correlation coefficient. On the other hand, emergent oscillations because of the inhibition of the feedback loop enhance the correlation in millisecond time scale and raise the correlation coefficient. In feedback spiking neural network for stimulus coding, these two opposing effects compete, and at some moderate gain value, one expects a trade-off where both effects play a significant role. And below or beyond that point, one effect is expected to dominate over the other, thereby setting the dependence of correlation on feedback gain. Furthermore, the non-monotonic relationship is proved to be independent of the network characteristics by varying input correlation coefficient, neuronal internal noise, network’s dynamic regime, and scale of neural populations. The effects of inhibitory feedback on correlated activity of neurons are well described by the non-monotonic curve.(4) The robustness of the correlated activity in the network is studied and the method to enhance the robustness is proposed. Early researches generally focus on homogeneous neural networks. Considering the heterogeneous biological neural system, the effect of heterogeneity on the correlated activity of the network is studied by distributing either the feedback gain or the firing threshold for each neuron according to Gaussian statistics. Simulation results show that heterogeneity can lower the correlation of the firing activity. However, in spite of moderate amount of heterogeneity, the oscillated activity and the non-monotonic relationship between the correlation coefficient of the network and the strength of the inhibitory feedback gain are robust. Moreover, the robustness of the correlated activity is independent of the type of heterogeneity. The oscillated activity in the network can be destroyed by great heterogeneity. The correlation coefficient of the network is thus decreased monotonically with the increasing of the strength of the inhibitory feedback gain. The non-monotonic relationship between the correlation coefficient and the feedback gain is existed due to the synchronized oscillations of the network. The robustness of the correlated activity can be enhanced by increasing the strength of inhibitory feedback gain. With strong inhibitory feedback, the correlated activity in the network modeled in this work is robust against heterogeneity, which is comparable to the heterogeneity observed in biological neural system.(5) Based on the inhibitory feedback models with either short-term synaptic depression or facilitation, the correlated activity in the network with varying synaptic time constants is discussed. The functions of short-term synaptic plasticity in correlated activity need further study, which is an essential feature of biological neural system. The short-term synaptic plasticity can change the strength of the inhibitory feedback gain, thus influences the correlated activity in the network. When the weak synaptic strength that is reduced by varying the synaptic time constants, leads to irregular firing activity, the correlation coefficient of the network depends on the amplitude of the neuronal response. When the network oscillates apparently due to the strong inhibitory feedback loop that is enhanced by varying synaptic time constants, the periodic activity determines the correlation coefficient of the network. The short-term synaptic plasticity is involved in neural coding by modulating the amplitude and regularity of the firing activity and changing the correlation in different time scale.