Mathematical Sciences: Analysis of Neural Networks: Stable Category Formation In A Complex Input Environment

卡彭特是一名研究人员，他打算开发和分析神经系统网络模型。这些模型将进行自组织模式识别和类别学习。作为正式的架构，模型将被转化为机器设计。作为神经网络，这些系统将基于心理和生理数据，并将用于分析模式识别和类别学习过程中的大脑和行为。从数学角度来看，这些模型是基于非线性的、奇异的、高维的常微分方程组。网络设计受到稳定性和适应性的相互冲突的要求以及复杂性的限制。给定任意复杂的输入序列，系统必须能够在没有老师的情况下提取稳定的类别。然而，该系统也必须保持可塑性，对新的学习持开放态度。新的网络设计将推广已经被证明能够以这样的方式对二进制输入模式的任意列表进行稳定编码的系统：在初始阶段之后，每个输入直接激活其类别表示。一旦学习完成，搜索机制就自动脱离。更通用的系统将对分级输入模式进行编码，并嵌入网络层次结构中，以适应自然和人工视觉和语音的特定约束。这个项目中描述的研究是高度跨学科的，因为它涉及神经网络科学、通信、机器人学和计算机视觉的某些方面、神经认知过程和数学。

CARPENTER The investigator intends to develop and analyze models of neural systems networks. These models will be designed to carry out a self-organizing pattern recognition and category learning. As formal architectures, the models will be translated into machine designs. As neural networks, the systems will be based on psychological and physiological data and will be used to analyze the brain and behavior in the process of pattern recognition and category learning. From a mathematical point of view, these models are based on nonlinear, singular, high dimensional systems of ordinary differential equations. Network design is constrained by the conflicting requirements of stability and adaptability, and by the complexity. Given an arbitrary complicated sequence of inputs, the system must be able to extract stable categories, without a teacher. However, the system must also remain plastic, open to new learning. New network designs will generalize systems which have been shown to stably encode arbitrary lists of binary input patterns in such a way that, after an initial phase, each input directly activates its category representation. The search mechanism is automatically disengaged once the learning is complete. The more general system will encode graded input patterns, and be embedded in network hierarchies adapted to the particular constraints of natural and artificial vision and speech. Research described in this project is highly cross-disciplinary, as it involves the neural networks science, communications, some aspects of robotics and computer vision, neural cognitive processes, and mathematics.