Song Yuru, Benna Marcus K
Neurosciences Graduate Program, University of California, San Diego, La Jolla, CA 92093, USA.
Department of Neurobiology, School of Biological Sciences, University of California San Diego, La Jolla, CA 92093, USA.
bioRxiv. 2024 Jul 4:2024.07.01.601490. doi: 10.1101/2024.07.01.601490.
Cortical neurons often establish multiple synaptic contacts with the same postsynaptic neuron. To avoid functional redundancy of these parallel synapses, it is crucial that each synapse exhibits distinct computational properties. Here we model the current to the soma contributed by each synapse as a sigmoidal transmission function of its presynaptic input, with learnable parameters such as amplitude, slope, and threshold. We evaluate the classification capacity of a neuron equipped with such nonlinear parallel synapses, and show that with a small number of parallel synapses per axon, it substantially exceeds that of the Perceptron. Furthermore, the number of correctly classified data points can increase superlinearly as the number of presynaptic axons grows. When training with an unrestricted number of parallel synapses, our model neuron can effectively implement an arbitrary aggregate transmission function for each axon, constrained only by monotonicity. Nevertheless, successful learning in the model neuron often requires only a small number of parallel synapses. We also apply these parallel synapses in a feedforward neural network trained to classify MNIST images, and show that they can increase the test accuracy. This demonstrates that multiple nonlinear synapses per input axon can substantially enhance a neuron's computational power.
皮层神经元通常会与同一个突触后神经元建立多个突触联系。为避免这些并行突触的功能冗余，每个突触具有独特的计算特性至关重要。在此，我们将每个突触对胞体的电流建模为其突触前输入的S型传递函数，具有诸如幅度、斜率和阈值等可学习参数。我们评估配备此类非线性并行突触的神经元的分类能力，并表明每个轴突具有少量并行突触时，其分类能力大大超过感知器。此外，随着突触前轴突数量的增加，正确分类的数据点数量可以超线性增加。当使用不受限制数量的并行突触进行训练时，我们的模型神经元可以有效地为每个轴突实现任意的聚合传递函数，仅受单调性约束。然而，模型神经元中的成功学习通常仅需要少量并行突触。我们还将这些并行突触应用于经过训练以对MNIST图像进行分类的前馈神经网络中，并表明它们可以提高测试准确率。这表明每个输入轴突的多个非线性突触可以显著增强神经元的计算能力。
