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

该项目旨在通过研究如何从神经活动（尖峰）和循环网络的连接性推断外部刺激之间的关系，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，这项研究将汇集两个互补的观点是什么控制感觉系统中的神经活动：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，可以直接从神经活动中构建刺激空间，从而绕过网络连接和感受野的知识，这些知识可能难以从大脑的一个区域传达到另一个区域。 这是通过使用一些来自代数拓扑和代数几何的优雅思想来实现的，这些思想在很大程度上是神经科学家所不知道的，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。 通过研究从递归神经网络和实验观察到的感受野中出现的活动模式之间的兼容性条件，该项目将找到对递归网络连接的约束，最终生成实验可检验的预测。 该理论框架也将被转化为新的数据分析工具，这将有助于分析大规模的电生理记录。神经科学的一个核心问题是理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揭示了神经活动和感官刺激之间的相关性，但对大脑如何编码相似类型的不同刺激之间的关系的理解很少。 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，典型的哺乳动物大脑区域，如新皮层和海马。 这些发现将对神经回路在学习和记忆中的作用以及大脑如何组织知识产生新的见解。 对神经回路的基本理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功能障碍有关。

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.