拉普拉斯神经流形的连续吸引子网络
Continuous Attractor Networks for Laplace Neural Manifolds
AI总结：
本文提出一种基于连续吸引子动力学的神经回路，通过边缘和凸起群体实现δ函数的拉普拉斯变换及其逆变换，并建模固定延迟的时序关联，该回路对噪声鲁棒，可用于多种认知模型。
摘要：
许多认知模型，包括那些用于预测未来事件时间的模型，都可以映射到一种特定的神经表征形式，其中神经元群体的活动被限制在流形上，这些流形指定了连续变量函数的拉普拉斯变换。这些编码拉普拉斯变换的群体与另一个群体相关联，后者对变换进行逆变换，近似还原原始函数。本文提出了一种神经回路，利用连续吸引子动力学来表示随时间演化的δ函数的拉普拉斯变换。一个群体在1维神经元阵列的任意位置放置一个边缘；另一个群体在与边缘对应的位置放置一个凸起。这两个群体共同可以估计时间上δ函数的拉普拉斯变换以及近似的逆变换。构建该回路使得边缘以适当速度移动，从而使网络能够将事件表示为对数时间的函数。在边缘网络内适当选择连接，使网络状态映射到随时间指数变化的拉普拉斯变换。在本文中，我们建模了一个学习的时间关联，其中一个刺激在固定延迟$T$后预测另一个刺激。在$t=0$之后不久，第一个刺激退入过去。表示过去的拉普拉斯神经流形维持拉普拉斯变换$\exp(-st)$。另一个拉普拉斯神经流形表示预测的未来。在$t=0$时，第二个刺激被表示为未来时间$T$。在0和$T$之间的每个时刻，预测未来的拉普拉斯变换上的放电变化为$\exp[-s(T-t)]$。尽管放电呈指数增长，该回路对噪声具有鲁棒性，使其成为在神经元群体中实现拉普拉斯神经流形以用于各种认知模型的实用手段。
英文摘要：
Many cognitive models, including those for predicting the time of future events, can be mapped onto a particular form of neural representation in which activity across a population of neurons is restricted to manifolds that specify the Laplace transform of functions of continuous variables. These populations coding Laplace transform are associated with another population that inverts the transform, approximating the original function. This paper presents a neural circuit that uses continuous attractor dynamics to represent the Laplace transform of a delta function evolving in time. One population places an edge at any location along a 1-D array of neurons; another population places a bump at a location corresponding to the edge. Together these two populations can estimate a Laplace transform of delta functions in time along with an approximate inverse transform. Building the circuit so the edge moves at an appropriate speed enables the network to represent events as a function of log time. Choosing the connections appropriately within the edge network make the network states map onto Laplace transform with exponential change as a function of time. In this paper we model a learned temporal association in which one stimulus predicts another at some fixed delay $T$. Shortly after $t=0$ the first stimulus recedes into the past. The Laplace Neural Manifold representing the past maintains the Laplace transform $\exp(-st)$. Another Laplace Neural Manifold represents the predicted future. At $t=0$, the second stimulus is represented a time $T$ in the future. At each moment between 0 and $T$, firing over the Laplace transform predicting the future changes as $\exp[-s(T-t)]$. Despite exponential growth in firing, the circuit is robust to noise, making it a practical means to implement Laplace Neural Manifolds in populations of neurons for a variety of cognitive models.
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