Profile
Robert Graham
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About Me:
I’m a first year PhD student in Mathematics at Lancaster, my research involves applying algebraic techniques to engineer symmetry-awareness AI systems. I have recently completed a 4 year undergraduate in Mathematics at Lancaster university.
Beyond mathematics, I enjoy spend my past time building lego, trekking around the rolling hills of Lancashire, and travelling all around the world.
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My pronouns are:
He/Him
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My Work:
I’m a PhD student researching the mathematics behind AI. AI might look like magic, but it’s really just maths. I’m also interested in post-quantum cryptography, because the world’s digital privacy depends on hard maths problems that future quantum computers might break.
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Read more
How does AI detect a cat in a photo?
Simple, we show it lots of pictures of cats. Sometimes millions of them. Over time, the AI learns what cats tend to look like.
But here’s a problem.
What if all the pictures we trained the AI on had the cat in the top-left corner of the image? If we then showed it a cat in the bottom-right corner, would it still recognise it?
Ideally, yes, because moving the cat around doesn’t change the fact that it’s still a cat.
In mathematics, moving something without changing what it is is called a symmetry. Sliding something across an image is one example of symmetry, called a translation.
My research is about teaching AI to understand these symmetries using algebra. If an AI knows that sliding an image shouldn’t change what it is looking at, it can recognise things in new situations it has never seen before.
This idea is called equivariance.
By building AI systems that understand different kinds of symmetry, like rotations, reflections, or other transformations, we can help them learn faster and generalise better. These ideas are useful across science, from robotics to discovering new proteins.
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My Interview