Mathis Alexander, Herz Andreas V M, Stemmler Martin B
Bernstein Center for Computational Neuroscience, and Department of Biology II, Ludwig-Maximilians-Universität München, 82152 Planegg-Martinsried, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022713. doi: 10.1103/PhysRevE.88.022713. Epub 2013 Aug 20.
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number N of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as 0.8. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with N is unaffected.
使用有噪声的计算单元对连续变量的信息进行编码是一项挑战；尽管如此，渐近理论表明，尽管存在噪声的干扰影响，但结合多个周期性尺度进行编码仍可具有高度的精确性[马西斯、赫茨和施泰姆勒，《物理评论快报》109, 018103 (2012)]。实际上，皮层似乎使用周期性的多尺度网格编码来精确表示位置。在此我们展示了如何在不采用长期极限的情况下读出此类编码；即使在短时间尺度上，此类编码的精度也会随着神经元数量N呈指数级变化。这一发现对于并非以统计独立方式发放冲动的神经元是否也成立呢？为了评估生物网格编码受统计相关性影响的程度，我们首先分析了行为啮齿动物中网格编码神经元对之间的噪声相关性。我们发现，如果两个神经元的网格对齐且具有相同长度尺度，那么神经元之间的噪声相关性可高达0.8。随着两个神经元网格之间不匹配程度的增加，噪声相关性迅速下降。将此类相关性纳入群体编码模型表明，相关性会降低分辨率，但分辨率随N的指数级变化不受影响。
