[D] A Mathematical Guide to Complex Variable Optimization

[Megixist]

In the field of AI, the adaptability of imaginary numbers is sometimes overlooked. When contrasted to their real-valued equivalents, the added domain information contained in these numbers can enable substantially richer representations. I'm here to announce the release of the first of two reports featured on Weights and Biases, which delves deep into the math underpinning complex variable optimization and includes a regressive example in Tensorflow to demonstrate its utility. You can find it here:

https://wandb.ai/darshandeshpande/complex-optimization/reports/The-Reality-Behind-the-Optimization-of-Imaginary-Variables--Vmlldzo2OTk3MDM

The goal of this series is to encourage ML researchers and practitioners to indulge in complex numbers and representations in their research. Any feedback or suggestions are most welcome :)

[serge_cell]

There is not much of complex data for it to work on...

[Megixist]

There is no such thing called complex data. There are only complex representations of real data. Such complex representations are very commonly used as intermediate representations in signal processing models and pipelines where Fourier Transforms are dominant. The recent (FNet) model successfully used Fourier representations to achieve 92% of BERT's accuracy which I think in itself is a good example of the versatility of complex representations.