RUI: Compressive Sensing and Neuronal Network Structure-Function Relationships

人类大脑是一个由数十亿神经元组成的复杂网络，这些神经元之间错综复杂的连接在很大程度上决定了感知和行为。因此，为了了解大脑的功能，有效地测量和分析神经网络结构是至关重要的。然而，测量大型神经网络的连通性在实验和理论上都是一个挑战。在复杂网络中重建连通性的一种更容易处理的方法是测量感兴趣的神经元的动态，然后使用数学方法来推断网络的连通性。该项目将利用在大脑网络中发现的广泛的稀疏性来开发一个有效的数学框架，用于从有限的神经元动力学测量中重建神经元连接。在准确地恢复神经元网络的结构后，该项目将研究自然刺激的稀疏结构如何影响神经元连接的早期发展，以及这在不同类别的感觉信号编码中的功能含义。该项目分析了网络连接和刺激信息的最佳编码神经元动力学，将为感觉处理和异常脑功能提供新的见解。在制定处理动态网络数据的新方法方面，该项目将为人工智能和假肢的进步提供信息。这项工作将积极地让本科生参与研究的各个阶段，促进跨学科的科学合作，并为不同的学生深化应用数学教育的范围。随着网络模型在数学科学中的日益普及，准确测量网络结构并理解其与网络函数的关系具有广泛的科学意义。特别是在神经科学中，有效地测量大规模的大脑连接并确定其对认知功能的影响是具有挑战性的，但也是表征大脑计算本质的基础。该项目将通过利用在大脑中发现的广泛的网络稀疏性和利用压缩感知（CS）理论的最新进展，为神经元连接的重建和表征制定一个新的框架。该项目的关键方面是：(1)基于嵌入在非线性网络动力学中的潜在输入输出映射，开发一种新的基于cs的平均场方法，用于有效地重建生理神经网络中的稀疏连接；(2)分析平衡网络运行制度在循环网络连通性CS重构中的作用；(3)通过神经元连接的监督学习研究视觉系统中结构基序的基础，以优化稀疏视觉刺激的压缩编码；(4)通过压缩网络动力学表征感受野结构在自然场景编码中的功能作用，以及在处理非自然场景（如虚幻图像）时相关缺陷的表现。这项工作将强调网络动态机制如何影响神经元动力学对结构连通性和网络输入的推断，提高可以确定神经元连通性的规模，并为大脑中的异常信息处理提供新的见解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The human brain is a complex network of billions of neurons whose intricate connectivity largely determines perception and behavior. To understand brain function, it is therefore paramount to efficiently measure and analyze neuronal network architecture. However, measuring the connectivity of large neuronal networks remains a challenge both experimentally and theoretically. An often more tractable approach to reconstructing connectivity in complex networks is to instead measure the dynamics of neurons of interest, and then use mathematical approaches to infer the network connectivity. This project will utilize the widespread sparsity found in brain networks to develop an efficient mathematical framework for reconstructing neuronal connectivity from limited measurements of neuronal dynamics. Upon accurately recovering the architecture of neuronal networks, this project will investigate how the sparse structure of natural stimuli impacts the early development of neuronal connectivity and what functional implication this has in the encoding of diverse classes of sensory signals. Analyzing the neuronal dynamics that optimally encode network connectivity and stimulus information, this project will provide new insights into sensory processing and abnormal brain function. In formulating novel methodologies for processing dynamic network data, this project will inform advances in artificial intelligence and prosthetics. This work will actively involve undergraduate students in all phases of research, promoting interdisciplinary scientific collaboration and deepening the scope of applied mathematics education for a diverse spectrum of students.With the increasing prevalence of network models in the mathematical sciences, accurately measuring network structure and understanding its relationship with network function is of broad scientific importance. In neuroscience in particular, efficiently measuring large-scale brain connectivity and determining its impact on cognitive function is inherently challenging yet fundamental in characterizing the nature of computation in the brain. This project will formulate a novel framework for the reconstruction and characterization of neuronal connectivity by taking advantage of the widespread network sparsity found in the brain and utilizing recent advances in compressive-sensing (CS) theory. Key facets of the project are to: (1) develop a novel CS-based mean-field approach for efficiently reconstructing sparse connections in physiological neuronal networks based on underlying input-output mappings embedded in the nonlinear network dynamics; (2) analyze the role of the balanced network operating regime in CS reconstruction of recurrent network connectivity; (3) investigate the basis for structural motifs in the visual system through supervised learning of neuronal connectivity aimed at optimized compressive encoding of sparse visual stimuli; and (4) characterize the functional role of receptive field structure in the encoding of natural scenes through compressive network dynamics and the manifestation of related deficiencies in processing non-natural scenes, such as illusory images. This work will underline how the network dynamical regime impacts the inference of structural connectivity and network inputs from neuronal dynamics, improving the scale over which neuronal connectivity can be determined and providing novel insights into abnormal information processing in the brain.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.