Single Layer HurNet: A Neural Network Without Backpropagation for Two-Dimensional Matrices

This paper introduces the Single Layer HurNet, a new artificial neural network architecture that operates without the need for backpropagation. Specifically designed for two-dimensional matrices, the Single Layer HurNet simplifies neural network structures by eliminating hidden layers and employing a direct method for calculating weights. Detailed mathematical formulations are presented to elucidate the underlying mechanisms of the network. We demonstrate that the Single Layer HurNet is capable of solving problems like the XOR logical operator, which are traditionally unsolvable by single-layer networks without hidden layers. Experimental results show that the Single Layer HurNet significantly outperforms traditional neural networks in training and inference speed, being over 3,150 times faster in certain cases. Future work aims to extend the HurNet to handle more complex data types by incorporating multi-layer concepts, which may result in performance gains in training Transformer-like networks.