Logistic Regression with Multi-Connected Weights

Abstract

Results of current research in biological and cognitive science reveal that neuronal interactions predominantly depend on neurotransmitters for signaling and sending information between neurons. Furthermore, a specific neuron that is connected to the next neuron transmits or sends multiple neurotransmitters in parallel ways, where each neurotransmitter has specific functional roles. Based on these results, a new type of logistic regression model is proposed that expands the dimensionality of connection weight coefficients from one to multiple coefficients, i.e., which means there are multiple connections between each input and hidden unit, rather than a single weight coefficient for every input unit. The number of dimensions of compound weights represents the number of various neurotransmitter categories and different weight components correspond to different neurotransmitter channels. According to recent biological studies, this new type of logistic regression model is promising to be much closer to a biological neuronal model. In terms of the new model structure in logistic regression with multidimensional weights, it is modeled on multiple filters and can enhance the interpretability of the sigmoid activation function of the learning algorithm. Results from computational experiments on CIFAR-10, CDC diabetes health indicators, and other benchmark datasets have shown that the performance of the existing logistic regression model can be enhanced by expanding the dimensionality of connected weights between each input unit and hidden unit and the approach of multiple weights will provide a new design architecture of models for artificial neural network architecture