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arXiv 2104.07059q-bio.NCcs.LG
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神经元群体几何:理解生物和人工神经网络的方法

Neural population geometry: An approach for understanding biological and artificial neural networks

Center for Theoretical Neuroscience, Columbia University(哥伦比亚大学理论神经科学中心)

SueYeon Chung, L. F. Abbott

摘要:

实验神经科学的进步已经改变了我们探索神经回路结构和功能的能力。与此同时,机器学习的进步释放了人工神经网络(ANN)的非凡计算能力。虽然这两个领域有不同的工具和应用程序,但它们提出了类似的挑战:即理解如何通过高维表示嵌入和处理信息,以解决复杂的任务。解决这一挑战的一种方法是利用数学和计算工具来分析这些高维表示的几何形状,即,神经元群体几何学。我们回顾了几何方法的例子,提供了深入了解生物和人工神经网络的功能:表示解开知觉,几何理论的分类能力,解开和抽象的认知系统,拓扑表示认知地图,动态解开运动系统,和一个动态的认知方法。总之,这些发现说明了机器学习,神经科学和几何学交叉的一个令人兴奋的趋势,其中神经元群体几何学提供了一个有用的群体级机械描述符底层任务的实现。重要的是,几何描述适用于感觉模态、大脑区域、网络架构和时间尺度。因此,神经元群体几何有可能统一我们对生物和人工神经网络的结构和功能的理解,弥合单个神经元,群体和行为之间的差距。

英文摘要:

Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial neural networks (ANNs). While these two fields have different tools and applications, they present a similar challenge: namely, understanding how information is embedded and processed through high-dimensional representations to solve complex tasks. One approach to addressing this challenge is to utilize mathematical and computational tools to analyze the geometry of these high-dimensional representations, i.e., neural population geometry. We review examples of geometrical approaches providing insight into the function of biological and artificial neural networks: representation untangling in perception, a geometric theory of classification capacity, disentanglement and abstraction in cognitive systems, topological representations underlying cognitive maps, dynamic untangling in motor systems, and a dynamical approach to cognition. Together, these findings illustrate an exciting trend at the intersection of machine learning, neuroscience, and geometry, in which neural population geometry provides a useful population-level mechanistic descriptor underlying task implementation. Importantly, geometric descriptions are applicable across sensory modalities, brain regions, network architectures and timescales. Thus, neural population geometry has the potential to unify our understanding of structure and function in biological and artificial neural networks, bridging the gap between single neurons, populations and behavior.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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