化学反应网络无需隐藏层即可超越含隐藏层的脉冲神经网络。
Chemical Reaction Networks Learn Better than Spiking Neural Networks
- 用确定性质量作用动力学证明无隐藏层的化学反应网络可完成复杂任务
- 数值实验显示其手写数字分类准确率和效率均优于带隐藏层的脉冲神经网络
- 为化学生物计算中的高效学习提供数学依据，适合对生物智能与计算模型交叉研究者
我们从数学上证明，不带隐藏层的化学反应网络能够解决需要脉冲神经网络引入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，我们证明了一个不带隐藏层的反应网络可以学习此前被证实需借助含隐藏层的脉冲神经网络才能实现的分类任务。我们提供了网络全局行为的解析后悔界，并分析了其渐近行为与Vapnik-Chervonenkis维度。在数值实验中，我们验证了所提化学反应网络在像素图像上对手写数字进行分类的能力，结果表明其在准确性和效率上均优于带有隐藏层的脉冲神经网络。这一发现为化学计算机中的机器学习提供了动机，并为生物细胞在生化反应网络中表现出比神经网络更高效学习行为提供了数学解释。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。