I realized that my other answer may have come off as rambling for someone not at all familiar with modern physics. Here's a summary:

Most modern physics, including Quantum Mechanics (QM) and General Relativity (GR) is represented primarily through "tensor fields" on a type of topological spaces called "manifolds". Tensor fields are like vector fields, just with tensors instead of vectors.

These tensor fields are then constrained by the laws of physics. At the core, these laws are really not so much "forces" as they're symmetries. The most obvious symmetries is that if you rotate or move all objects within a space, the physics should be unaltered. Now if you also insist that the speed of light should be identical in all frames of reference, you basically get Special Relativity (SR) from that.

The forces of electromagnetism, weak and strong force follow from invariance under the combined U(1) x SU(2) x SU(3) symmetries. (Gravity is not considered a real force in General Relativity (GR), but rather as interaction between spacetime and matter/energy, and what we observe as Gravity is similar to time dilation of SR, but with curved space)

Ok. This may be abstract if you're not familiar with it, and even more if you're not familiar with Group Theory. But it will be referenced further down.

"Manifolds" are a subset of topological spaces that are Euclidian or "flat" locally. This flatness is important, because it's basically (if I understand it correctly myself) the reason why we can use linear algebra for local effects.

I will not go into GR here, since that's what I know least well, but instead focus on QM which describes the other 3 forces.

In QM, there is the concept of the "Wave Function" which is distributed over space-time. This wave-function is really a tensor with components that give rise to observable fields, such as magnetism, the electric field and to the weak and strong forces. (The tensor is not the observed fields directly, but a combination of a generalization of the fields and also analogues to electric charge, etc.)

So how physics calculations tends to be done, is that one starts with assuming something like an initial state, and then impose the symmetries that correspond to the forces. For instance, two electrons wavefunctions may travel towards the same point from different directions.

The symmetries will then dictate what the wave function looks like at at each later incremental point in time. Computationally, such increments are calculated for each point in space using tensor multiplication.

While this is "local" in space, points in space immediately next to the point we're calculating for need to be include, kind of like for convolutional nets.

Basically, though, it's in essence a tensor multiply for each point in space to propagate the wave function from one point in time to the immediate next point.

Eventually, once the particles have (or have not) hit each other, the wave functions of each will scatter in all directions. The probability for it to go in any specific direction is proportional to the wave function amplitude in that direction, squared.

Since doing this tensor multiplication for every point in space requires infinite compute, a lot of tricks are used to reduce the computation. And this where a lot of our intuitions about "particles" show up. For simple examples, one can even do very good approximations using calculus. But fundamentally, tensor multiplication is the core of Quantum Mechanics.

This approach isn't unique to QM, though. A lot of other Physics is similar. For instance, solid state physics, lasers or a lot of classical mechanics can be described in similar frameworks, also using tensors and symmetry groups. (My intuition is that this still is related to Physics involving local effects on "locally flat" Manifolds)

And this translates all the way up to how one would do the kind of simulations of aspects of physical worlds that happen in computer games inside GPU's, including the graphics parts.

And here I believe you may see how the circle is starting to close. Simulations and predictions of physical systems at many different levels of scale and abstraction tend to reduce to tensor multiplication of various sorts. While the classical physics one learns in high school tend to have problems solvable with calculus, even those are usually just solutions to problems that are fundamentally linear algebra locally.

While game developers or ML researches initially didn't use the same kind of Group Theory machinery that Physics have adapted, at least the ML side seem to be going in that direction, based on texts such as:

https://maurice-weiler.gitlab.io/cnn_book/EquivariantAndCoor...

(There appears to be a lot of similar findings over the last 5-6 years or so, that I wasn't fully aware of).

In the book above, the methodology used is basically identical to how theoretical physics approach similar problems, at least for networks that describe physical reality (which CNNs tends to be good for)

And here is my own (current) hypothesis why this also seems to be extendable to things like LMM, that do not at face value appear like physics problems:

If we assume that the human brain evolved the ability to navigate the physical world BEFORE it developed language (should be quite obvious), it should follow that the type of compute fabric in the brain should start out as optimized for the former. In practice, that means that at the core, the neural network architecture of the brain should be good at doing operations similar to tensor products (or approximations of such).

And if we assume that this is true, it shouldn't be surprising that when we started to develop languages, those languages would take on a form that were suitable to be processed in compute fabric similar to what was already there. To a lesser extent, this could even be partially used to explain why such networks can also produce symbolic math and even computer code.

Now what the brain does NOT seem to be evolved to do, is what traditional Turing Machine computers are best at, namely do a lot very precise procedural calculations. That part is very hard for humans to learn to do well.

So in other words, the fact that physical systems seem to involve tensor products (without requiring accuracy) may be the explanation to why Neural Networks seem to have a large overlap with the human brain in terms of strengths and weaknesses.