Wu Si, Hamaguchi Kosuke, Amari Shun-Ichi
Department of Informatics, University of Sussex, Brighton BN1 9QH, U.K.
Neural Comput. 2008 Apr;20(4):994-1025. doi: 10.1162/neco.2008.10-06-378.
Continuous attractor is a promising model for describing the encoding of continuous stimuli in neural systems. In a continuous attractor, the stationary states of the neural system form a continuous parameter space, on which the system is neutrally stable. This property enables the neutral system to track time-varying stimuli smoothly, but it also degrades the accuracy of information retrieval, since these stationary states are easily disturbed by external noise. In this work, based on a simple model, we systematically investigate the dynamics and the computational properties of continuous attractors. In order to analyze the dynamics of a large-size network, which is otherwise extremely complicated, we develop a strategy to reduce its dimensionality by utilizing the fact that a continuous attractor can eliminate the noise components perpendicular to the attractor space very quickly. We therefore project the network dynamics onto the tangent of the attractor space and simplify it successfully as a one-dimensional Ornstein-Uhlenbeck process. Based on this simplified model, we investigate (1) the decoding error of a continuous attractor under the driving of external noisy inputs, (2) the tracking speed of a continuous attractor when external stimulus experiences abrupt changes, (3) the neural correlation structure associated with the specific dynamics of a continuous attractor, and (4) the consequence of asymmetric neural correlation on statistical population decoding. The potential implications of these results on our understanding of neural information processing are also discussed.
连续吸引子是一种很有前景的模型，用于描述神经系统中连续刺激的编码。在连续吸引子中，神经系统的静止状态形成一个连续的参数空间，系统在该空间上是中性稳定的。这一特性使中性系统能够平稳地跟踪随时间变化的刺激，但它也会降低信息检索的准确性，因为这些静止状态很容易受到外部噪声的干扰。在这项工作中，基于一个简单的模型，我们系统地研究了连续吸引子的动力学和计算特性。为了分析一个原本极其复杂的大型网络的动力学，我们利用连续吸引子能够非常快速地消除垂直于吸引子空间的噪声分量这一事实，开发了一种降低其维度的策略。因此，我们将网络动力学投影到吸引子空间的切线上，并成功地将其简化为一个一维的奥恩斯坦 - 乌伦贝克过程。基于这个简化模型，我们研究了：（1）在外部噪声输入驱动下连续吸引子的解码误差；（2）当外部刺激发生突然变化时连续吸引子的跟踪速度；（3）与连续吸引子特定动力学相关的神经相关结构；以及（4）不对称神经相关性对统计群体解码的影响。我们还讨论了这些结果对我们理解神经信息处理的潜在意义。
