This paper describes a novel approach to synthesize molecular reactions to train a perceptron, i.e., a single-layered neural network, with sigmoidal activation function. The approach is based on fractional coding where a variable is represented by two molecules. The synergy between fractional coding in molecular computing and stochastic logic implementations in electronic computing is key to translating known stochastic logic circuits to molecular computing. In prior work, a DNA perceptron with bipolar inputs and unipolar output was proposed for inference. The focus of this paper is on synthesis of molecular reactions for training of the DNA perceptron. A new molecular scaler that performs multiplication by a factor greater than 1 is proposed based on fractional coding. The training of the perceptron proposed in this paper is based on a modified backpropagation equation as the exact equation cannot be easily mapped to molecular reactions using fractional coding.

中文翻译：

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通过分数编码训练 DNA 感知器

本文描述了一种合成分子反应以训练感知器的新方法，即具有 sigmoidal 激活函数的单层神经网络。该方法基于分数编码，其中变量由两个分子表示。分子计算中的分数编码与电子计算中的随机逻辑实现之间的协同作用是将已知的随机逻辑电路转换为分子计算的关键。在之前的工作中，提出了一种具有双极输入和单极输出的 DNA 感知器用于推理。本文的重点是合成用于训练 DNA 感知器的分子反应。基于分数编码，提出了一种新的分子缩放器，它可以执行大于 1 的因子的乘法。