Relating stimulus space geometry and topology to neural network activity and connectivity

这个项目试图通过研究如何从神经活动(棘波)和递归网络的连通性来推断外部刺激之间的关系，来加深我们对大脑如何创建刺激空间表示的理解。在这样做的过程中，这项研究将把控制感觉系统中神经活动的两个互补的视角结合在一起：感受野和神经网络动力学。在与Carina Curto的合作中，我们开发了一种新的理论方法，能够直接从神经活动建立刺激空间，从而绕过网络连接和接受场的知识，这些知识可能难以从大脑的一个区域交流到另一个区域。这是利用神经科学家基本不知道的代数拓扑和代数几何中的一些优秀思想实现的，并为分析递归神经网络的结构和功能开辟了一条新的途径。通过调查循环神经网络产生的活动模式与实验观察到的感受野之间的兼容性条件，该项目将找到对循环网络连通性的限制，最终产生可实验测试的预测。该理论框架还将转化为新的数据分析工具，将有助于分析大规模电生理记录。神经科学中的一个中心问题是了解大脑如何创造外部世界的表征。虽然大量的实验工作已经发现了神经活动和感觉刺激之间的相关性，但对于大脑如何编码不同类型的类似刺激之间的关系，人们知之甚少。这项研究开发了一个新的理论框架来研究这个问题，通过研究刺激编码和递归神经回路结构之间的相互作用，这些神经回路是哺乳动物大脑区域的典型，如新皮质和海马体。这些发现将为神经回路在学习和记忆中的作用以及大脑如何组织知识提供新的见解。对神经回路的基本了解的进展对于提高我们对学习障碍和疾病(如癫痫和精神分裂症)的理解至关重要，这些疾病被认为与神经回路的故障有关。

This project seeks to deepen our understanding of how the brain creates representations of stimulus spaces by studying how relationships between external stimuli can be inferred from the neural activity (spikes) and connectivity of a recurrent network. In doing so, this research will bring together two complementary perspectives on what controls neural activity in sensory systems: receptive fields and neural network dynamics. In joint work with Carina Curto, we have developed a novel theoretical approach that enables building stimulus spaces directly from neural activity, thus circumventing knowledge of network connectivity and of receptive fields that may be difficult to communicate from one area of the brain to another. This is achieved using some elegant ideas from algebraic topology and algebraic geometry that are largely unknown to neuroscientists, and opens up a new avenue for the analysis of the structure and function of recurrent neural networks. By investigating compatibility conditions between patterns of activity emerging from recurrent neural networks and experimentally observed receptive fields, this project will find constraints on recurrent network connectivity, ultimately generating experimentally testable predictions. The theoretical framework will also be translated into novel data analysis tools that will be useful for in analyzing large-scale electrophysiological recordings. A central question in neuroscience is to understand how the brain creates representations of the external world. Although a great deal of experimental work has uncovered correlations between neural activity and sensory stimuli, there is very little understanding of how the brain encodes relationships between distinct stimuli of similar type. This research develops a novel theoretical framework to investigate this question by studying the interplay between stimulus encoding and the structure of recurrent neural circuits, typical of mammalian brain areas such as neocortex and hippocampus. The findings will yield new insight into the role of neural circuits in learning and memory, and of how the brain organizes knowledge. Progress in the basic understanding of neural circuits is essential for improving our understanding of learning disabilities and diseases (such as epilepsy and schizophrenia) that are believed to be related to the malfunction of neural circuits.