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Register a new userMolecular and DNA Artificial Neural Networks via Fractional Coding
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This paper considers implementation of artificial neural networks (ANNs) using molecular computing and DNA based on fractional coding. Prior work had addressed molecular two-layer ANNs with binary inputs and arbitrary weights. In prior work using fractional coding, a simple molecular perceptron that computes sigmoid of scaled weighted sum of the inputs was presented where the inputs and the weights lie between [-1, 1]. Even for computing the perceptron, the prior approach suffers from two major limitations. First, it cannot compute the sigmoid of the weighted sum, but only the sigmoid of the scaled weighted sum. Second, many machine learning applications require the coefficients to be arbitrarily positive and negative numbers that are not bounded between [-1, 1]; such numbers cannot be handled by the prior perceptron using fractional coding. This paper makes four contributions. First molecular perceptrons that can handle arbitrary weights and can compute sigmoid of the weighted sums are presented. Thus, these molecular perceptrons are ideal for regression applications and multi-layer ANNs. A new molecular divider is introduced and is used to compute sigmoid(ax) where a > 1. Second, based on fractional coding, a molecular artificial neural network (ANN) with one hidden layer is presented. Third, a trained ANN classifier with one hidden layer from seizure prediction application from electroencephalogram is mapped to molecular reactions and DNA and their performances are presented. Fourth, molecular activation functions for rectified linear unit (ReLU) and softmax are also presented.
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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.
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