To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, there is no satisfactory synthesis of core principles that lead to multi-modular grid cells in deep recurrent neural networks. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: coding theory, dynamical systems, function optimization and supervised deep learning. We then leverage our insights to propose a new approach that combines the strengths of all four approaches. Our approach is a self-supervised learning (SSL) framework - including data, data augmentations, loss functions and a network architecture - motivated from a normative perspective, without access to supervised position information or engineering of particular readout representations as needed in previous approaches. We show that multiple grid cell modules can emerge in networks trained on our SSL framework and that the networks and emergent representations generalize well outside their training distribution. This work contains insights for neuroscientists interested in the origins of grid cells as well as machine learning researchers interested in novel SSL frameworks.

翻译：为了解决映射、定位和导航的空间问题，哺乳动物演化出了显著的空间表示能力。其中一种重要的空间表示是获得诺贝尔奖的网格细胞：这些神经元以看似奇异、具有几个离散周期的非局部和空间周期性活动模式，表征自我位置这一局部且非周期性的量。哺乳动物为何会学习这种奇特的网格表示？数学分析表明，这种多周期表示作为一种具有高容量和内在纠错能力的代数编码具有优异特性，但迄今为止，尚无令人满意的核心原则综合能够解释深度递归神经网络中多模网格细胞的产生机制。在本工作中，我们首先从编码理论、动力系统、函数优化和监督式深度学习四类研究范式中提炼出关于网格细胞问题的关键洞见。随后借助这些洞见，提出一种融合四类方法优势的新方案。该方案是基于规范视角的自监督学习（SSL）框架——包含数据、数据增强、损失函数和网络架构——无需如先前方法那样依赖监督位置信息或特定读出表征的工程化设计。我们证明，基于该SSL框架训练的网络能够涌现出多个网格细胞模块，并且网络及其涌现的表征在训练分布之外仍具有良好泛化能力。本研究既为关注网格细胞起源的神经科学家提供洞见，也为研究新型SSL框架的机器学习研究者带来启示。