AF: Small: An Algorithmic Theory of Brain Behavior: Concept Representation and Learning in Spiking Neural Networks

这个项目旨在通过抽象的、交互的、分布式的算法来理解大脑中的计算。它假设了一个基于有向图（节点和连接边）的计算数学模型，其中节点对应神经元，边缘对应神经元可以相互影响的神经纤维。该项目研究的问题是由实际大脑解决的典型问题，例如集中注意力、做出决策、检测感知气味或视觉场景之间的相似性，以及识别和学习具有有趣结构的概念。它使用理论计算机科学的技术来研究这些问题。这项工作有生物学和计算机科学的双重动机。算法的视角有望帮助理解生物神经网络所采用的计算机制。另一方面，这些网络解决的许多问题也是计算机科学和人工智能的基础问题；在生物神经网络的背景下研究它们有望提供一个新的视角并产生新的结果。生物算法具有天生的灵活性、鲁棒性和适应性——这些特性也是现代计算机系统所需要的。更详细地说，这项工作是基于一个同步的、随机的峰值神经网络（SNN）模型。此前，研究者和合作者使用这种类型的模型研究了几个问题，包括赢家通吃的决策，数据压缩和聚类，以及简单层次结构概念的学习。他们提出了新的算法（网络），并根据网络规模和收敛时间等成本对其进行了分析。他们还发现了一些成本权衡，并证明了相关的下界结果。这个项目继续这个研究项目，但现在关注的核心问题是概念是如何在大脑中表征的，这些表征是如何被使用的，以及它们是如何被学习的。这里的“概念”既包括逻辑概念，如层次结构和语言结构，也包括物理概念，如移动的物体。一个主要论点是：“现实世界概念中自然存在的结构反映在它们的神经表征中，以一种促进学习和识别的方式。”该项目使用理论计算机科学的方法，特别是分布式和概率算法，以及线性代数和复杂性理论，来研究这一假设。该项目的另一个重点是噪音和不确定性如何影响大脑网络中解决问题的成本，以及表征的选择。还有一个是关于大脑如何将解决简单问题的网络组合成解决更复杂问题的更大的网络。具体来说，该项目正在研究(1)关于SNN模型及其计算能力的基本理论问题，(2)可能用于解决更复杂的大脑问题的常见神经原语（如赢者通吃），(3)关于大脑网络中结构化概念的有效静态表示的问题，以及(4)关于如何学习这些表示的问题。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。

This project aims at understanding computation in the brain, in terms of abstract, interacting, distributed algorithms. It assumes a mathematical model of computation based on directed graphs (nodes and connecting edges), where the nodes correspond to neurons and the edges correspond to nerve fibers by which neurons may influence each other. The project studies problems that are typical of those solved by actual brains, such as problems of focusing attention, making decisions, detecting similarity between sensed odors or visual scenes, and recognizing and learning concepts with interesting structure. It studies these problems using techniques from theoretical computer science. This work has both biological and computer-science motivations. The algorithmic perspective is expected to help in understanding the computational mechanisms employed by biological neural networks. On the other hand, many of the problems that are solved by these networks are also fundamental in computer science and artificial intelligence; studying them in the setting of biological neural networks is expected to offer a new perspective and yield new results. Biological algorithms are naturally flexible, robust, and adaptive---properties that are also desirable for modern computer systems.In more detail, this work is based on a synchronous, stochastic Spiking Neural Network (SNN) model. Previously, the investigator and collaborators used this type of model to study several problems including Winner-Take-All decision-making, data compression and clustering, and learning of simple hierarchically-structured concepts. They produced new algorithms (networks) and analyzed them in terms of costs such as network size and convergence time. They also discovered some cost tradeoffs and proved related lower bound results. This project continues this research program, but now focusing on the central issues of how concepts are represented in the brain, how those representations are used, and how they may be learned. "Concepts" here encompass both logical concepts, such as hierarchical structures and linguistic constructs, and physical concepts, such as moving objects. A main thesis is: "Structure that is naturally present in real-world concepts gets mirrored in their neural representations, in a way that facilitates both learning and recognition." This project uses approaches from theoretical computer science, notably, distributed and probabilistic algorithms, as well as linear algebra and complexity theory, to investigate this hypothesis. Another emphasis of the project is on how noise and uncertainty affect the costs of solving problems in brain networks, as well as the choice of representations. Still another is on how the brain may combine networks that solve simpler problems into larger networks that solve more complex problems. Specifically, the project is studying (1) fundamental theoretical questions about SNN models and their computing power, (2) common neural primitives (such as Winner-Take-All) that may be used to solve more complex brain problems, (3) questions about efficient static representations of structured concepts in brain networks, and (4) questions about how such representations can be learned.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.