We study the learning problem associated with spiking neural networks.
Specifically, we consider hypothesis sets of spiking neural networks with
affine temporal encoders and decoders and simple spiking neurons having only
positive synaptic weights. We demonstrate that the positivity of the weights
continues to enable a wide range of expressivity results, including
rate-optimal approximation of smooth functions or approximation without the
curse of dimensionality. Moreover, positive-weight spiking neural networks are
shown to depend continuously on their parameters which facilitates classical
covering number-based generalization statements. Finally, we observe that from
a generalization perspective, contrary to feedforward neural networks or
previous results for general spiking neural networks, the depth has little to
no adverse effect on the generalization capabilities.

我们研究了与尖峰神经网络相关的学习问题，具体来说，我们考虑具有仿射时间编码器和解码器以及仅具有正向突触权重的简单尖峰神经元的尖峰神经网络的假设集。我们证明了正权重尖峰神经网络的广泛表达性结果，包括对平滑函数的速率最优逼近或无维度诅咒的逼近。此外，正权重尖峰神经网络被证明在其参数上连续依赖，这有助于传统的基于覆盖数量的泛化语句。最后，我们观察到，从泛化的角度来看，与前馈神经网络或以前的针对通用尖峰神经网络的结果相反，深度对泛化能力几乎没有不利影响。