We mathematically prove that chemical reaction networks without hidden layers can solve tasks for which spiking neural networks require hidden layers. Our proof uses the deterministic mass-action kinetics formulation of chemical reaction networks. Specifically, we prove that a certain reaction network without hidden layers can learn a classification task previously proved to be achievable by a spiking neural network with hidden layers. We provide analytical regret bounds for the global behavior of the network and analyze its asymptotic behavior and Vapnik-Chervonenkis dimension. In a numerical experiment, we confirm the learning capacity of the proposed chemical reaction network for classifying handwritten digits in pixel images, and we show that it solves the task more accurately and efficiently than a spiking neural network with hidden layers. This provides a motivation for machine learning in chemical computers and a mathematical explanation for how biological cells might exhibit more efficient learning behavior within biochemical reaction networks than neuronal networks.

翻译：我们通过数学证明表明，无隐藏层的化学反应网络能够解决需要脉冲神经网络借助隐藏层才能完成的任务。该证明基于化学反应网络的确定性质量作用动力学模型。具体而言，我们证明某一无隐藏层的反应网络可以学会先前被证明需借助隐藏层的脉冲神经网络才能实现的分类任务。我们给出了该网络全局行为的解析遗憾界，并分析了其渐近行为与Vapnik-Chervonenkis维度。在数值实验中，我们验证了所提出的化学反应网络对像素图像中手写数字的分类学习能力，并证明其比带隐藏层的脉冲神经网络更精确高效地解决了该任务。这为化学计算机中的机器学习提供了理论依据，并从数学角度解释了生物细胞为何可能在生化反应网络中表现出比神经元网络更高效的学习行为。