so deep learning is 100s of millions or more data points. Gather that along with some hierarchical hidden markov model artificial neural nets in the order of 100s if millions of neurons to feed through the data sets and your chat interface. Run all that as a cloud service. Publish an ARC plug in for it and you are in business.

Apologies, I do not understand the question. Cortana is not a deep learning engine. Deep learning is less than half of any application. There doesn't seem to be an example of what you would be searching for, or what you would be storing.

You can find out more about Cortana on Microsoft's website. It is similar to Siri and connects operating system events to recognized spoken phrases. Here is a description of what Cortana does: https://en.m.wikipedia.org/wiki/Cortana_(software)

As for "cloud based", that only means a majority of the processing is performed on a remote computer over a network connection. The only advantage to cloud based software is the data is accessible from any network location with a device supporting the client software.