Collaborative Research: Emergent Sequences in Inhibition-Dominated Recurrent Networks

合作研究：抑制主导的循环网络中的涌现序列

• 批准号: 1951599
• 负责人: Katherine Morrison
• 金额: $ 16.32万
• 依托单位: University of Northern Colorado
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1951599&HistoricalAwards=false
• 关键词: Collaborative; Research; Emergent; Sequences; Inhibition

Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. Moreover, sequences that occur in hippocampus while the animal is at rest or asleep are believed to be critical for memory processing and consolidation. These sequences are examples of internally generated activity: that is, neural activity that is shaped primarily by the structure of recurrent connections between neurons. The goal of this research is to advance the mathematical theory of sequence generation. A fundamental question is what types of network architectures underlie emergent sequences. This work will investigate the mechanisms for sequence generation in recurrently connected networks with complex patterns of connectivity and inhibition-dominated dynamics. The theory will then be used to understand and model neural sequences, with a focus on hippocampal sequences. Although this work is motivated by neuroscience, the phenomenon of sequential activity emerging from competition between units is sufficiently common that the mathematical results derived here are likely to be useful in a variety of broader contexts in the biological and social sciences.The main goal of this research is to understand, and be able to predict, the set of neural activity sequences in a recurrent network from the underlying structure of connectivity. In addition to providing new insights about sequence generation in the brain, this study will elucidate structure-function relationships in recurrent networks and provide tools for analyzing networks to identify dynamically relevant motifs. This research will be carried out in the context of a special family of inhibition-dominated threshold-linear networks, which are a commonly used firing rate model of recurrent network dynamics. These networks naturally give rise to an abundance of sequences, and the dynamics are tightly connected to the underlying connectivity graph. Moreover, they are mathematically tractable and thus amenable to a mathematical theory of sequence generation. Project 1 focuses on network architectures built from directional graphs, a new type of graph exhibiting directional dynamics without necessarily having a feedforward architecture, thus providing an important generalization of synfire chains. Project 2 addresses the anatomy of a sequence and its decomposition into “core” and “peripheral” components, with the core being a network motif that supports a sequential attractor, and the periphery consisting of additional neurons that are recruited by the attractor. Finally, Project 3 uses the theory developed in earlier projects to analyze and model various phenomena observed in hippocampal sequences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

神经活动的序列出现在许多大脑区域，包括皮层、海马体和构成运动等有节奏行为的中央模式产生电路。此外，当动物处于休息或睡眠状态时，海马体中发生的序列被认为是记忆处理和巩固的关键。这些序列是内部产生的活动的例子：即主要由神经元之间经常性连接的结构塑造的神经活动。本研究的目的是推进序列生成的数学理论。一个基本的问题是，什么类型的网络架构是应急序列的基础。这项工作将研究具有复杂的连通性模式和抑制主导的动力学的递归连接网络中的序列生成机制。然后，该理论将被用来理解神经序列并对其进行建模，重点是海马体序列。虽然这项工作是由神经科学推动的，但由于单元之间的竞争而产生的顺序活动的现象非常普遍，因此这里得到的数学结果很可能在生物和社会科学的各种更广泛的背景下有用。本研究的主要目标是从连通性的底层结构来理解并能够预测递归网络中的神经活动序列集。除了为大脑中的序列生成提供新的见解外，这项研究还将阐明循环网络中的结构-功能关系，并提供分析网络以识别动态相关基序的工具。本研究将在一类特殊的以抑制为主的阈值线性网络的背景下进行，这类网络是递归网络动力学中常用的发放率模型。这些网络自然会产生大量的序列，并且动态与底层的连接图紧密相连。此外，它们在数学上很容易处理，因此服从序列生成的数学理论。项目1专注于从有向图构建的网络体系结构，有向图是一种新型的图，展示了方向动态而不一定具有前馈体系结构，因此提供了对Synfire链的重要概括。项目2研究序列的解剖及其分解为“核心”和“外围”部分，核心是支持顺序吸引子的网络基元，外围由吸引子招募的额外神经元组成。最后，项目3使用早期项目中开发的理论来分析和模拟在海马区序列中观察到的各种现象。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Graph Rules for Recurrent Neural Network Dynamics

递归神经网络动力学的图规则

• DOI: 10.1090/noti2661
• 发表时间: 2023
• 期刊: Notices of the American Mathematical Society
• 作者: Curto, Carina;Morrison, Katherine
• 通讯作者: Morrison, Katherine

Nerve Theorems for Fixed Points of Neural Networks

神经网络不动点的神经定理

• DOI: 10.1007/978-3-030-95519-9_6
• 发表时间: 2022
• 期刊: Association for Women in Mathematics series
• 作者: Santander, D. E.;Ebli, S.;Patania, A.;Sanderson, N.;Burtscher, F.;Morrison, K.;Curto, C.
• 通讯作者: Curto, C.