One of the most difficult tasks in the modern computing age is performing efficient network analysis and optimization. I spoke with Arjun Ramani, an 18-year-old mathematician who is working on that problem, to better understand his new method for dealing with it. He’s building a better mousetrap, if you will, for identifying important anomalies within any network.
Arjun has been funding his research, partially, through awards for his work. I learned about him after reading the results of the 2017 Regeneron Science Talent Search, where he was awarded $150,000 to put towards his research.
After chatting for a few minutes about his work. I asked what was special about it, he told me “it’s the most efficient way to create random networks for the Kronecker model” and when I asked how he could back that claim up — he pointed to the math.
His findings are impressive
Arjun told me that his research was conducted in ‘creating algorithms that would increase efficiency.’ I stopped him right there. He had me at algorithms, I stumbled my way into a question about machine-learning and he said “Well, I guess there’s some applications there.”
While describing the work he’s doing Arjun sent me a paper that explained he was taking the Kronecker Method for a form of nonstandard matrix multiplication that allows someone to simulate how networks evolve over time, and exploiting the mathematics behind it to create random networks.
Arjun put it in a way I could understand, he had me imagine a triangle with each point being part of a network. Eureka; if there’s one thing I know it’s shapes.
His work, he explained, allowed for the creation of random networks that resembled my triangle network, these random networks provided all the information I needed to compare my network’s performance to, in order for me to understand what’s unusual or what I should expect from my network. I understood the triangle part perfectly.
Don’t we already analyze networks?
The applications are already there, we’re already doing what Arjun is talking about – we just aren’t doing it very efficiently. A neuro-surgeon who is trying to map the neural network of a patient might not have access to a server farm that can give him enough power to run the necessary processes required for the network to be entirely understood.
Using Arjun’s method you could simulate any number of randomly generated networks to compare yours to, and you can do it fast. Our neuro-surgeon is no longer limited by the number of patient’s heads they can personally scan.
This is how network engineers predict the future – and Arjun wants to make that process faster and more efficient. He’s hacking a mathematical method from 1882 to make it work better for the world of 2017.
It’s one thing to have a social network like Facebook, it’s entirely different trying to figure out what happens next for Facebook. If you make sprockets, and all of your competitors make sprockets, you can analyze your ‘sprocket network’ against your competitors.
Arjun’s work will, theoretically, let you simulate what a million other randomly generated Facebooks would look like so that you can start looking for patterns in yours, or Mark Zuckerberg’s as the case may be.
You’re going to be using his math tomorrow
I’m certain that Arjun and the people working with him will get a little grin out of my interpretations, but all my doe-eyed-awe aside – this is real work with real applications being conducted by more than just Arjun. He works in conjunction with Assistant Professor David Gleich, from Purdue University, a guy who has spent his career coming up with quicker and smarter ways to do big idea stuff.
The future might be robots and civilian space-travel and science fiction delights galore – but it’s all going to work through networking. Social-media networks, AI networks, every possible network – you’ll be using the results of Arjun’s genius in the future.
What’s next for the math wizard? “Extending the algorithms into hyper-graphs.” He says. I didn’t ask for an explanation; my brain was already full for the day.