Efficient and flexible representation of higher-dimensional cognitive variables with grid cells
Efficient and flexible representation of higher-dimensional cognitive variables with grid cells
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DOI：
10.1371/journal.pcbi.1007796
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发表时间：
2020-04-01
影响因子：
4.3
通讯作者：
Fiete, Ila
中科院分区：
文献类型：
--
作者：
Klukas, Mirko;Lewis, Marcus;Fiete, Ila
作者摘要哺乳动物的内嗅网格细胞由其放电场的周期性排列定义，并在二维空间信息的表示中发挥着重要作用。同时，它们代表了多种非空间认知变量。因此，很自然地要问网格单元理论上可以表示什么类型和维度的变量。我们证明，网格单元可以提供一个神经向量空间，用于明确的积分、记忆和表示比二维高得多的各种不同（欧几里得）变量，而不需要更高维的网格状响应。同一电路可以灵活地表示不同维度的变量，具有高动态范围和低神经成本，无需对循环电路进行任何重新配置。我们揭示了内嗅网格细胞有效编码大于二维的变量的潜力，同时保持其低维结构的经验数据。我们的模型通过低维随机投影和“经典”低维六边形网格单元响应的组合来构造高维输入的表示。无需重新配置循环电路，同一系统可以灵活地编码不同维度的多个变量，同时通过自动权衡维度与指数级大的编码范围来最大化编码范围（每个维度）。它通过结合模块化和混合选择性这两个强大的概念（我们称之为“混合模块化编码”）来实现高效率和灵活性。与之前提出的方案相比，该模型不需要形成高维网格响应，这是一种细胞效率低下且僵化的机制。在飞行的蝙蝠或攀爬的老鼠中观察到的发射场可以由结合多个网格模块活动的神经元生成，根据我们的模型，每个网格模块代表更高维度的空间。这个想法扩展了我们对网格单元的理解，表明它们可以实现一个通用电路，为高维向量空间中的变量生成按需编码和存储状态。
Author summaryEntorhinal grid cells in mammals are defined by the periodic arrangement of their firing fields and play a major role in the representation of 2D spatial information. At the same time, they represent a variety of non-spatial cognitive variables. It is thus natural to ask what kinds and dimensions of variables it is theoretically possible for grid cells to represent. We show that grid cells can provide a neural vector space for unambiguous integration, memory, and representation of a variety of different (Euclidean) variables of much higher dimension than two, without requiring higher-dimensional grid-like responses. The same circuit can flexibly represent variables of different dimensions, doing so with high dynamic range and at low neural cost, without any reconfiguration of the recurrent circuitry.We shed light on the potential of entorhinal grid cells to efficiently encode variables of dimension greater than two, while remaining faithful to empirical data on their low-dimensional structure. Our model constructs representations of high-dimensional inputs through a combination of low-dimensional random projections and "classical" low-dimensional hexagonal grid cell responses. Without reconfiguration of the recurrent circuit, the same system can flexibly encode multiple variables of different dimensions while maximizing the coding range (per dimension) by automatically trading-off dimension with an exponentially large coding range. It achieves high efficiency and flexibility by combining two powerful concepts, modularity and mixed selectivity, in what we call "mixed modular coding". In contrast to previously proposed schemes, the model does not require the formation of higher-dimensional grid responses, a cell-inefficient and rigid mechanism. The firing fields observed in flying bats or climbing rats can be generated by neurons that combine activity from multiple grid modules, each representing higher-dimensional spaces according to our model. The idea expands our understanding of grid cells, suggesting that they could implement a general circuit that generates on-demand coding and memory states for variables in high-dimensional vector spaces.