Bedenbaugh P, Gerstein G L
Department of Neuroscience, University of Pennsylvania, School of Medicine, Philadelphia 19104-6085.
Biol Cybern. 1994;70(3):219-25. doi: 10.1007/BF00197602.
We investigated the normalized autocovariance (correlation coefficient) function of the output of an erf() function nonlinearity subject to non-zero mean Gaussian noise input. When the sigmoid is wide compared to the input, or the input mean is close to the midpoint of the sigmoid, the output correlation coefficient function is very close to the input correlation coefficient function. When the noise mean and variance are such that there is a significant probability of operating in the saturation region and the sigmoid is not too flat, the correlation coefficient of the output function is less than that of the input. This difference is much greater when the correlation coefficient is negative than when it is positive. The sigmoid partially rectifies the correlation coefficient function. The analysis does not depend on the spectral properties of the input noise. All that is required is that the input at times t and (t + tau) be jointly gaussian with the same mean and autocovariance. The analysis therefore applies equally well to the case of two identical sigmoids with jointly gaussian inputs. This correlational rectification could help explain the parameter sensitivity of "neural network" models. If biological neurons share this property it could explain why few negative correlations between spike trains have been observed.
我们研究了在非零均值高斯噪声输入下，erf()函数非线性输出的归一化自协方差（相关系数）函数。当Sigmoid函数相对于输入较宽，或者输入均值接近Sigmoid函数的中点时，输出相关系数函数非常接近输入相关系数函数。当噪声均值和方差使得在饱和区域运行有显著概率且Sigmoid函数不太平坦时，输出函数的相关系数小于输入的相关系数。当相关系数为负时，这种差异比为正时大得多。Sigmoid函数部分校正了相关系数函数。该分析不依赖于输入噪声的频谱特性。所需要的只是在时刻t和(t + τ)的输入与相同均值和自协方差的联合高斯分布。因此，该分析同样适用于具有联合高斯输入的两个相同Sigmoid函数的情况。这种相关校正有助于解释“神经网络”模型的参数敏感性。如果生物神经元具有这种特性，这可以解释为什么在尖峰序列之间很少观察到负相关。
