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Incorporating biological neuronal properties into Artificial Neural Networks(ANNs) to enhance computational capabilities poses a formidable challenge inthe field of machine learning. Inspired by recent findings indicating thatdendrites adhere to quadratic integration rules for synaptic inputs, we proposea novel ANN model, Dendritic Integration-Based Quadratic Neural Network(DIQNN). This model shows superior performance over traditional ANNs in avariety of classification tasks. To reduce the computational cost of DIQNN, weintroduce the Low-Rank DIQNN, while we find it can retain the performance ofthe original DIQNN. We further propose a margin to characterize thegeneralization error and theoretically prove this margin will increasemonotonically during training. And we show the consistency betweengeneralization and our margin using numerical experiments. Finally, byintegrating this margin into the loss function, the change of test accuracy isindeed accelerated. Our work contributes a novel, brain-inspired ANN model thatsurpasses traditional ANNs and provides a theoretical framework to analyze thegeneralization error in classification tasks.

Dendritic Integration Based Quadratic Neural Networks Outperform Traditional Aritificial Ones