Fully tensorial approach to hypercomplex neural networks

Fully tensorial theory of hypercomplex neural networks is given. It allows neural networks to use arithmetic based on arbitrary algebras. The key point is to observe that algebra multiplication can be represented as a rank three tensor and use this tensor in every algebraic operation. This approach is attractive for neural network libraries that support effective tensorial operations. It agrees with previous implementations for four-dimensional algebras.

@article{niemczynowicz2025_2407.00449,
  title={ Fully tensorial approach to hypercomplex neural networks },
  author={ Agnieszka Niemczynowicz and Radosław Antoni Kycia },
  journal={arXiv preprint arXiv:2407.00449},
  year={ 2025 }
}