Lorentz Transformation Neural Network

We propose a novel neural network architecture, the Lorentz Transformation Neural Network (LTNN), which utilizes Lorentz transformations to generate a complex computation matrix that enhances the network’s expressive power. Furthermore, LTNN is lightweight due to the shared weight matrices in the computation matrix. LTNN treats the input and output as coordinates in high-dimensional spacetime, with the weight matrices in each layer representing the velocity components of a spacetime reference frame. During training, these weight matrices are transformed into a computation matrix via Lorentz transformations, describing the coordinate transformations between different reference frames. We evaluate LTNN on four datasets: California Housing Prices, Iris, MNIST, and Fashion-MNIST. Experimental results demonstrate that LTNN outperforms conventional neural networks and quaternion neural networks in terms of both accuracy and parameter efficiency.