amen zwa, esq.<p>In <a href="https://mathstodon.xyz/tags/EE" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EE</span></a>, we tend to see information as a time-varying, <a href="https://mathstodon.xyz/tags/complex" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>complex</span></a> signal, with the magnitude conveying the content and the phase the context. We received this tradition from the mathematicians and the physicists who preceded us by a few centuries. And this perspective is bashed into our little brains, from the very first semester of our undergraduate curricula.</p><p>The complex representation affords greater information capacity and many analytical conveniences. As such, most everything we do is in the complex domain \(\mathbb{C}\): electric machines, transmission lines, electromagnetics, DSP, DIP, etc. This habit even affects the way we use our HP RPN calculators. In short, we adore complex numbers. But this perspective is not shared by our <a href="https://mathstodon.xyz/tags/CS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CS</span></a> and <a href="https://mathstodon.xyz/tags/DS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DS</span></a> brethren.</p><p>Modern DNNs are inhered with might processing powers. These powers can be further enhanced by adapting real-valued NNs (rvNNs) as complex-valued NNs (cvNNs). Real-valued time-domain signal can be converted to complex signal, using Hilbert transform.</p><p>Sure, Liouville’s Theorem had long stood in the way of convergence of cvNNs. But over the past four decades, the EE community had devised many workarounds. Hirose describes cvNNs in his 2012 book. I do believe CS and DS communities should at least glance at cvNNs.</p><p><a href="https://link.springer.com/book/10.1007/978-3-642-27632-3" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">link.springer.com/book/10.1007</span><span class="invisible">/978-3-642-27632-3</span></a></p>