标题： 高分辨率的空间记忆需要类似网格细胞的神经编码 显示英文标题

标题： High-resolution spatial memory requires grid-cell-like neural codes

摘要： 连续吸引子网络（CANs）被广泛用于模拟大脑如何通过持续的循环活动暂时保留连续的行为变量，例如动物在环境中的位置。 然而，这种记忆机制对即使是很小的缺陷也非常敏感，例如噪声或异质性，这些在生物系统中都很常见。 以前的研究表明，将连续体离散化为一组有限的离散吸引子状态可以提高对这些缺陷的鲁棒性，但必然会降低所表示变量的分辨率，从而在稳定性和分辨率之间产生权衡。 我们表明，对于使用单峰凸起类似编码的CANs，如传统模型中的情况，这种稳定性和分辨率的权衡最为严重。 为了克服这一点，我们研究了基于随机特征嵌入的稀疏二进制分布式编码，其中神经元具有空间周期性的感受野。 我们通过理论和仿真证明，这样的网格细胞类似编码使CANs能够同时实现高稳定性和高分辨率。 该模型扩展到将任意非线性流形嵌入到CAN中，例如球体或环面，并将线性路径积分推广到沿自由编程的流形上向量场的积分。 总之，这项工作提供了一种理论，说明大脑如何以高分辨率稳健地表示连续变量，并在任务相关的流形上执行灵活的计算。 显示英文摘要

摘要： Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory mechanism is very sensitive to even small imperfections, such as noise or heterogeneity, which are both common in biological systems. Previous work has shown that discretising the continuum into a finite set of discrete attractor states provides robustness to these imperfections, but necessarily reduces the resolution of the represented variable, creating a dilemma between stability and resolution. We show that this stability-resolution dilemma is most severe for CANs using unimodal bump-like codes, as in traditional models. To overcome this, we investigate sparse binary distributed codes based on random feature embeddings, in which neurons have spatially-periodic receptive fields. We demonstrate theoretically and with simulations that such grid-cell-like codes enable CANs to achieve both high stability and high resolution simultaneously. The model extends to embedding arbitrary nonlinear manifolds into a CAN, such as spheres or tori, and generalises linear path integration to integration along freely-programmable on-manifold vector fields. Together, this work provides a theory of how the brain could robustly represent continuous variables with high resolution and perform flexible computations over task-relevant manifolds.