通过神经曼菲尔德动力学实现通用计算

IF 2.7 4区 计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Joan Gort
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引用次数: 0

摘要

越来越多的证据表明,许多形式的神经计算可能是通过在群体尺度上展开的低维动力学来实现的。然而,目前人们对这些内嵌动态过程的连接结构和一般能力都不甚了解。在这项研究中,我们使用分析、拓扑学和非线性动力学工具对两种最常见的发射率模型形式进行了评估,以便为这些问题提供合理的解释。研究表明,在所有这些模型中,低等级结构连通性预示着不变流形和全局吸引流形的形成。关于这些流形中产生的动力学,研究证明它们在所考虑的各种形式中具有拓扑等价性。这封信还表明,在低阶假设下,神经流形(包括输入驱动系统)中出现的流动是普遍的,这拓宽了之前的发现。它探讨了低维轨道如何承载肌肉轨迹连续集的产生、中心模式发生器的实现以及记忆状态的存储。这些动力学可以在任意有界记忆串上稳健地模拟任何图灵机,实际上赋予了速率模型以通用计算的能力。此外,这封信还展示了低阶假说是如何预测皮层活动中观察到的相关结构的。最后,它还讨论了这一理论如何为使用数学方法研究神经心理学现象提供有用的工具。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Emergence of Universal Computations Through Neural Manifold Dynamics
There is growing evidence that many forms of neural computation may be implemented by low-dimensional dynamics unfolding at the population scale. However, neither the connectivity structure nor the general capabilities of these embedded dynamical processes are currently understood. In this work, the two most common formalisms of firing-rate models are evaluated using tools from analysis, topology, and nonlinear dynamics in order to provide plausible explanations for these problems. It is shown that low-rank structured connectivities predict the formation of invariant and globally attracting manifolds in all these models. Regarding the dynamics arising in these manifolds, it is proved they are topologically equivalent across the considered formalisms. This letter also shows that under the low-rank hypothesis, the flows emerging in neural manifolds, including input-driven systems, are universal, which broadens previous findings. It explores how low-dimensional orbits can bear the production of continuous sets of muscular trajectories, the implementation of central pattern generators, and the storage of memory states. These dynamics can robustly simulate any Turing machine over arbitrary bounded memory strings, virtually endowing rate models with the power of universal computation. In addition, the letter shows how the low-rank hypothesis predicts the parsimonious correlation structure observed in cortical activity. Finally, it discusses how this theory could provide a useful tool from which to study neuropsychological phenomena using mathematical methods.
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来源期刊
Neural Computation
Neural Computation 工程技术-计算机:人工智能
CiteScore
6.30
自引率
3.40%
发文量
83
审稿时长
3.0 months
期刊介绍: Neural Computation is uniquely positioned at the crossroads between neuroscience and TMCS and welcomes the submission of original papers from all areas of TMCS, including: Advanced experimental design; Analysis of chemical sensor data; Connectomic reconstructions; Analysis of multielectrode and optical recordings; Genetic data for cell identity; Analysis of behavioral data; Multiscale models; Analysis of molecular mechanisms; Neuroinformatics; Analysis of brain imaging data; Neuromorphic engineering; Principles of neural coding, computation, circuit dynamics, and plasticity; Theories of brain function.
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