Mathematical Modeling of Attention and Consciousness by Using Layered Neural Networks

利用人工神经网络研究大脑的记忆、学习、注意、意识等高级功能，对于理解和阐明高等动物大脑的信息处理能力具有重要意义。这些研究课题是人类的终极课题之一。我们的研究小组一直试图为大脑中那些高级功能的数学建模迈出一步，包括视觉注意力等等。研究结果如下：(1)基于Desimone和Duncan的假设，构建了基于FitHugh-Nagumo方程的脉冲神经元双层神经网络模型，研究了视觉选择性注意。也就是说，这两层由海马体形成层和视觉皮层组成。我们发现，视觉选择性注意是这些层上神经元在频率和放电时间上的同步现象（见参考文献10）。(2)采用霍奇金-赫胥黎神经元构建双层神经网络模型，研究了视觉选择性注意。(见参考。(11))。(3)注意和意识现在正在研究中，他们利用克里克的假设和德西蒙和邓肯的假设构建了一个数学模型。(准备。)(4)研究了动态神经网络模型的记忆召回。例如，我们利用该模型成功地完成了自联想记忆的回忆和异联想记忆的回忆。(见参考文献。（五）、（六）、（七）(5)通过构建FitzHugh-Nagumo神经元双层神经网络模型，研究了theta和gamma振荡的产生。（见参考文献(8)）(6)研究了工作记忆、学习、MST神经元和光流等。(1)-(3)及(9)。

Studies on higher function in brain such as memory, learning, attention and consciousness by using artificial neural networks are so important for understanding and clarification of information processing ability in brains of animals of higher orders. Those research subjects are one of ultimate themes of mankind. Our research group has been tried to give a step for mathematical modeling for those higher function in the brain including visual attention and so on. Some of the obtained results in the present project are as follows:(1) We investigated visual selective attention by constructing of two-layered neural network model with spiking neurons described by FitHugh-Nagumo equation, based on a hypothesis given by Desimone and Duncan. Namely the two layers consist of a layer of hippocampal formation and that of visual cortex. We found that the visual selective attention is the synchronous phenomena for a frequency and also firing time between neurons on those layers (See Ref. (10).)(2) We investigated visual selective attention by using Hodgkin-Huxley neurons for the two-layered neural network model. (See Ref.(11).)(3) Attention and consciousness are now under investigation by constructing a mathematical model using the hypothesis by Crick and the one by Desimone and Duncan. (In preparation.)(4) We investigated the memory recall in dynamical neural network models. For example, we succeeded in the autoassociative memory recall and also the heteroassociative memory recall by using the proposed model. (See Refs.(5), (6) and (7).)(5) We investigated the emergence of the theta and the gamma oscillation by constructing a two-layered neural network model with FitzHugh-Nagumo neurons. (See Ref. (8).)(6) fe investigated working memory, learning, MST neurons for optical flows and so on, (See Refs.(1)-(3) and (9).)