@article{complexstochasticgradientdescentanddirec,
  title = {Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces},
  author = {Natanael Alpay and Emeric Battaglia},
  year = {2026},
  eprint = {2604.23017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2604.23017},
}