Makito Oku

Chaos in neurons and its application: Perspective of chaos engineering

We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaneys chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.

Pseudo-Orthogonalization of Memory Patterns for Associative Memory

A new method for improving the storage capacity of associative memory models on a neural network is proposed. The storage capacity of the network increases in proportion to the network size in the case of random patterns, but, in general, the capacity suffers from correlation among memory patterns. Numerous solutions to this problem have been proposed so far, but their high computational cost limits their scalability. In this paper, we propose a novel and simple solution that is locally computable without any iteration. Our method involves XNOR masking of the original memory patterns with random patterns, and the masked patterns and masks are concatenated. The resulting decorrelated patterns allow higher storage capacity at the cost of the pattern length. Furthermore, the increase in the pattern length can be reduced through blockwise masking, which results in a small amount of capacity loss. Movie replay and image recognition are presented as examples to demonstrate the scalability of the proposed method.

NUMERICAL ANALYSIS OF TRANSIENT AND PERIODIC DYNAMICS IN SINGLE AND COUPLED NAGUMO–SATO MODELS

The Nagumo–Sato (NS) model is a one-dimensional piecewise linear map that describes simplified dynamics of a single neuron. The NS model and its network extension, coupled Nagumo–Sato models, exhibit complex behavior both in their transient dynamics and after converging to periodic orbits. However, the way the period and the transient length change against the parameters is not completely understood. In this study, we numerically investigate the transient and periodic dynamics in single and coupled NS models. Simulation results indicate the following observations. (1) The period of a single NS model shows layered structures associated with the Farey sequence. (2) Two coupled NS models show discontinuity in the transient length, even though the period does not change. (3) In the case of an associative memory model consisting of NS models, there exists a small parameter region where both the period and the transient length increase considerably. The dynamics within the region is much more complex than that outside the region.

Traveling Waves in Locally Connected Chaotic Neural Networks and Their Phenomenological Modeling

The emergence of traveling waves is a universal property of nervous systems. However, mechanisms of these waves and their functional roles have not yet been fully elucidated. Here, we numerically investigate traveling waves in a locally connected large-scale chaotic neural network (CNN) consisting of more than one million units. We simulate it by parallel computing and visualize the network output by using color images. If the refractoriness of neurons is sufficiently large, many local cell assemblies are generated and the boundaries between them move as traveling waves. We also develop a simplified phenomenological model for the CNN by adding a negative self-feedback mechanism to the Potts model. The proposed meso-scopic model can qualitatively reproduce complex wave patterns in the CNN. Because the model requires less computational resources, it may serve as a useful tool for investigating traveling waves in nervous systems.

Dynamical coherence patterns in neural field model at criticality

Phase synchronization is a mechanism that plays a crucial role in information processing in the brain, and coherence is one of the factors used to evaluate the pairwise degree of phase synchronization. Coherence is also an important measure for examining brain functions because it implies communication and cooperation among neurons. In this work, we study the coherence patterns of spontaneous activity in a neural field model at criticality where a second-order phase transition occurs with special properties that differentiate it from other regions. The results are summarized as follows. First, in high-frequency bands, the system outside the critical region is unable to communicate efficiently via phase synchronization. Second, the dynamical coherence patterns at the criticality show switching between high and low coherence states. Finally, we found that in a very brief period, there is high broadband coherence between some pairs of spatial points. This phenomenon can be observed only in the critical region.

A mathematical model of planning in the prefrontal cortex

The prefrontal cortex (PFC) is involved in many complex cognitive functions such as problem-solving, planning, reasoning, and decision-making. However, the biological mechanisms of these computations are not clear. To understand these mechanisms, we theoretically consider the experimental result of a path-planning task by Mushiake et al. using a mathematical model referred to as the potential network model. The simulation results show that our model can take the correct path in most trials, regardless of the goal positions and the block patterns in the task. Furthermore, our model reproduces the characteristics of the neuronal activity in both the PFC and the primary motor cortex. This study reveals that although the potential network model is abstract, it can be useful in modelling higher brain functions.

Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint

In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks.

Networked reinforcement learning

Recently, many models of reinforcement learning with hierarchical or modular structures have been proposed. They decompose a task into simpler subtasks and solve them by using multiple agents. However, these models impose certain restrictions on the topological relations of agents and so on. By relaxing these restrictions, we propose networked reinforcement learning, where each agent in a network acts autonomously by regarding the other agents as a part of its environment. Although convergence to an optimal policy is no longer assured, by means of numerical simulations, we show that our model functions appropriately, at least in certain simple situations.