Masahiko Yoshioka

Spike-timing-dependent learning rule to encode spatiotemporal patterns in a network of spiking neurons

We study associative memory neural networks based on the Hodgkin-Huxley type of spiking neurons. We introduce the spike-timing-dependent learning rule, in which the time window with the negative part as well as the positive part is used to describe the biologically plausible synaptic plasticity. The learning rule is applied to encode a number of periodical spatiotemporal patterns, which are successfully reproduced in the periodical firing pattern of spiking neurons in the process of memory retrieval. The global inhibition is incorporated into the model so as to induce the gamma oscillation. The occurrence of gamma oscillation turns out to give appropriate spike timings for memory retrieval of discrete type of spatiotemporal pattern. The theoretical analysis to elucidate the stationary properties of perfect retrieval state is conducted in the limit of an infinite number of neurons and shows the good agreement with the result of numerical simulations. The result of this analysis indicates that the presence of the negative and positive parts in the form of the time window contributes to reduce the size of crosstalk term, implying that the time window with the negative and positive parts is suitable to encode a number of spatiotemporal patterns. We draw some phase diagrams, in which we find various types of phase transitions with change of the intensity of global inhibition.

Spike-timing-dependent synaptic plasticity to learn spatiotemporal patterns in recurrent neural networks

Assuming asymmetric time window of the spike-timingdependent synaptic plasticity (STDP), we study spatiotemporal learning in recurrent neural networks. We first show numerical simulations of spiking neural networks in which spatiotemporal Poisson patterns (i.e., random spatiotemporal patterns generated by independent Poisson process) are successfully memorized by the STDP-based learning rule. Then, we discuss the underlying mechanism of the STDP-based learning, mentioning our recent analysis on associative memory analog neural networks for periodic spatiotemporal patterns. Order parameter dynamics in the analog neural networks explains time scale change in retrieval process and the shape of the STDP time window optimal to encode a large number of spatiotemporal patterns. The analysis further elucidates phase transition due to destabilization of retrieval state. These findings on analog neural networks are found to be consistent with the previous results on spiking neural networks. These STDP-based spatiotemporal associative memory possibly gives some insights into the recent experimental results in which spatiotemporal patterns are found to be retrieved at the various time scale.

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons.

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatiotemporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatiotemporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with function is reduced to the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.

Oscillator neural network model with distributed native frequencies

We study the associative memory of an oscillator neural network with distributed native frequencies. The model is based on the Hebbian learning rule. The distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to become entirely synchronized, long time behaviours of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations.