A unified theory for the origin of grid cells through the lens of pattern formation
A unified theory for the origin of grid cells through the lens of pattern formation
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发表时间：
2019
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通讯作者：
Ben Sorscher;Gabriel C. Mel;S. Ganguli;Samuel A. Ocko
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作者：
Ben Sorscher;Gabriel C. Mel;S. Ganguli;Samuel A. Ocko
大脑中的网格细胞在空间中以惊人的规则六边形模式放电。目前有两个看似不相关的框架来理解这些模式。机制模型占六边形的发射场的结果，图案形成动态的循环神经网络与手动调整的中心-环绕连接。规范模型指定了一个神经架构，一个学习规则和一个导航任务，并观察到网格状的激发场由于解决这个任务的约束而出现。在这里，我们提供了一个分析理论，统一了两个角度，铸造的学习动力学的神经网络训练的导航任务作为一个模式形成的动力系统。该理论提供了对规范性任务的不同配方的最佳解决方案的洞察，并表明空间表示中的对称性正确地预测了经过训练的神经网络中学习的射击场的结构。此外，我们的理论证明，一个非负约束的发射率诱导一个破坏机制，有利于六角形的发射场。我们将这一理论扩展到学习多个网格地图的情况下，并证明了最佳解决方案包括一个层次结构的地图与增加的长度尺度。这些结果统一了以前的帐户的网格细胞发射，并提供了一个新的框架，预测学习表示的递归神经网络。
Grid cells in the brain fire in strikingly regular hexagonal patterns across space. There are currently two seemingly unrelated frameworks for understanding these patterns. Mechanistic models account for hexagonal firing fields as the result of pattern-forming dynamics in a recurrent neural network with hand-tuned center-surround connectivity. Normative models specify a neural architecture, a learning rule, and a navigational task, and observe that grid-like firing fields emerge due to the constraints of solving this task. Here we provide an analytic theory that unifies the two perspectives by casting the learning dynamics of neural networks trained on navigational tasks as a pattern forming dynamical system. This theory provides insight into the optimal solutions of diverse formulations of the normative task, and shows that symmetries in the representation of space correctly predict the structure of learned firing fields in trained neural networks. Further, our theory proves that a nonnegativity constraint on firing rates induces a symmetry-breaking mechanism which favors hexagonal firing fields. We extend this theory to the case of learning multiple grid maps and demonstrate that optimal solutions consist of a hierarchy of maps with increasing length scales. These results unify previous accounts of grid cell firing and provide a novel framework for predicting the learned representations of recurrent neural networks.