Tal D, Schwartz E L
Department of Cognitive and Neural Systems, Boston University, MA 02215, USA.
Neural Comput. 1997 Feb 15;9(2):305-18. doi: 10.1162/neco.1997.9.2.305.
The leaky integrate-and-fire (LIF) model of neuronal spiking (Stein 1967) provides an analytically tractable formalism of neuronal firing rate in terms of a neuron's membrane time constant, threshold, and refractory period. LIF neurons have mainly been used to model physiologically realistic spike trains, but little application of the LIF model appears to have been made in explicitly computational contexts. In this article, we show that the transfer function of a LIF neuron provides, over a wide-parameter range, a compressive nonlinearity sufficiently close to that of the logarithm so that LIF neurons can be used to multiply neural signals by mere addition of their outputs yielding the logarithm of the product. A simulation of the LIF multiplier shows that under a wide choice of parameters, a LIF neuron can log-multiply its inputs to within a 5% relative error.
神经元放电的泄漏积分发放（LIF）模型（斯坦因，1967年）依据神经元的膜时间常数、阈值和不应期，提供了一种易于进行分析处理的神经元放电率形式体系。LIF神经元主要用于对生理上逼真的放电序列进行建模，但在明确的计算环境中，LIF模型的应用似乎很少。在本文中，我们表明，在较宽的参数范围内，LIF神经元的传递函数提供了一种与对数函数足够接近的压缩非线性，使得LIF神经元能够通过简单相加其输出（得到乘积的对数）来对神经信号进行乘法运算。对LIF乘法器的模拟表明，在广泛的参数选择下，LIF神经元能够对其输入进行对数乘法运算，相对误差在5%以内。
