Way back when, I did a masters in physics. I learned a lot of math: vectors, a ton of linear algebra, thermodynamics (aka entropy), multi-variable and then tensor calculus.

This all turned out to be mostly irrelevant in my subsequent programming career.

Then LLMs came along and I wanted to learn how they work. Suddenly the physics training is directly useful again! Backprop is one big tensor calculus calculation, minimizing… entropy! Everything is matrix multiplications. Things are actually differentiable, unlike most of the rest of computer science.

It’s fun using this stuff again. All but the tensor calculus on curved spacetime, I haven’t had to reach for that yet.

Check out this 156-page tome: https://arxiv.org/abs/2104.13478: "Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges"

The intro says that it "...serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented."

Working all the way through that, besides relearning a lot of my undergrad EE math (some time in the previous century), I learned a whole new bunch of differential geometry that will help next time I open a General Relativity book for fun.

That past work will pay off even more when you start looking into diffusion and flow-based models for generating images, videos, and sometimes text.

For me, it's the very basics of general relativity which made the distinction between the cotangent and tangents space click. Optimisation on Riemannian manifolds might give an opportunity to apply more interesting tensor calculus with a non-trivial metric.

I have the same experience but with a masters in control theory. Suddenly all the linear algebra and differential equations are super useful in understanding this.

Any reason you didn't pick up computer graphics before? Everything is linear algebra and there's even actual physics involved.

Well, calculus on curved space, please let me introduce you to: https://arxiv.org/abs/2505.18230 (This is self advertising) If you know how to incorporate time into that, I am interested.

The funny thing about physics maths, is that we didn't have to learn the intuition behind it, it was a mean to an end. Going through undergrad mathematically blind was a right of passage.

Modern numeric compute frameworks provide automatic differentiation to calculate derivatives, including Tensorflow and Jax.

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