Mathematical Sciences: "Analog Neural Networks and Delay Equations".

数学科学：“模拟神经网络和延迟方程”。

• 批准号: 9622722
• 负责人: Tomas Gedeon
• 金额: $ 6万
• 依托单位: Montana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622722&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analog; Neural; Networks

Gedeon 9622722 Analog neural networks admit stationary, periodic and chaotic solutions. So far the stationary solutions have received most attention of researchers. However, in recent years the importance of non-stationary patterns in brain became clear. The investigator studies networks which admit periodic orbits and addresses the apparent discrepancy between discrete and continuous time networks of this type. While in continuous networks one expects generally a convergence to a periodic orbit, in discrete time networks there are stable stationary solutions. The project investigates chaotic behaviour of a class of networks with step-function nonlinearities. These can be viewed as a limiting case of a steep sigmoid nonlinearities and are easier to handle analytically. The delay in synaptic response of a neuron is a recognized fact; if one wants to account for its affect the appropriate model must be expressed in terms of delay differential equation. The investigator studies the discretization of this equation and shows that this finite-dimensional approximation captures the essential features of the dynamics of the delay equation. Artificial neural networks is an area on a crossroads between artificial inteligence and neurobiology. Mathematical models play an important role in this area. Neural networks try to model some basic functions of brain (learning, recognizing trained patterns) without trying to understand the intricate details of how the neurons work on a chemical or physiological level. Neural networks are used today in many areas of apllied science and engineering. The network can be trained to recognize a certain pattern, given slightly perturbed data. This pattern must be stationary, i.e. fixed in time. On the other hand, there is hardly any process in the brain which is stationary, and most processes are periodic. The investigator studies networks that admit periodic patterns, to understand the relationship between differen t models and see which one is the most suitable for applications. If one were able to train the networks to recognize complicated patterns (in space and time), that would have an immediate impact on robotics and artificial inteligence.

Gedeon 9622722 模拟神经网络承认固定，周期和混沌的解决方案。 到目前为止，稳态解受到了研究者的极大关注。 然而，近年来，非平稳模式在大脑中的重要性变得越来越明显。 调查研究网络承认周期轨道和地址之间的明显差异离散和连续时间网络的这种类型。 虽然在连续网络中，人们通常期望收敛到周期轨道，但在离散时间网络中，存在稳定的稳态解。 该项目研究一类具有阶跃函数非线性的网络的混沌行为。 这些可以被看作是一个陡峭的S形非线性的限制情况下，更容易处理分析。 神经元突触反应的延迟是一个公认的事实，如果要解释它的影响，必须用延迟微分方程来表示适当的模型。 研究人员研究了这个方程的离散化，并表明，这种有限维近似捕获的延迟方程的动态的基本特征。 人工神经网络是介于人工智能和神经生物学之间的一个交叉点。 数学模型在这一领域发挥着重要作用。 神经网络试图模拟大脑的一些基本功能（学习，识别训练模式），而不试图理解神经元在化学或生理水平上如何工作的复杂细节。 神经网络今天被用于应用科学和工程的许多领域。 该网络可以被训练来识别某种模式，只要数据稍微受到干扰。 这种模式必须是静止的，即在时间上固定的。 另一方面，大脑中几乎没有任何过程是静止的，大多数过程都是周期性的。 研究人员研究了承认周期性模式的网络，以了解不同模型之间的关系，并确定哪一个最适合应用。 如果能够训练网络识别复杂的模式（空间和时间），这将对机器人技术和人工智能产生直接影响。