At the end of my undergrad, I remember a UW professor being poached by intel to work on analogue computing research project, the chair of the department at the time said that it was an opportunity that might not ever happen again and he had to take. I don’t think it went anywhere (since I never heard of intel coming out with a product), but I at least knew there was an attempt.

Yes I too am perplexed. I'm into audio synthesis so I feel I have somewhat better-than-average knowledge of oscillators, from the component or elementary mathematical level (depending on whether they're analog or digital) to complex interactions for fun and profit (frequency, phase, ring modulation).

These are cool results but I was disappointed not to find any discussion of where oscillator array technology stands today what the manufacturing challenges/opportunities might be. It seems like it would be prohibitively expensive for anything beyond minimal networks of a few hundred nodes that could be used in sensors. Even if you have perfectly consistent oscillators that synchronize to each other within very fine tolerances, wiring them up to each other is still a massive headache.

The oscillating elements don't map directly to pixels. Conventional models also have n^2 parameters.

What they are trying to achieve is to demonstrate that the coupling approach works in a simulated physics environment (O(n^2) as you point out) so that they can then build CMOS circuits that create actual oscillators and then let the laws of physics do the computation. This is a very bold vision!

It seems like total parameter count is more or less on par with conventional approaches so any gains won't be from there.

We can implement coupled oscillators in hardware but are the couplings and frequencies programmable? If they're being streamed in I guess you'd still have a memory bandwidth bottleneck and associated energy usage. If not then the fair comparison is to a conventional model hardcoded in an ASIC which AFAIU is actually quite energy efficient.

(Disclaimer, not my area of expertise.) It appears to be adjacent but more general. There's an entire collection of methods (including reservoir computing) that conceptually resemble or are based on physical systems in one way or another. This appears to be an attempt to develop a new method that natively takes place as a physical process that we could readily implement in hardware.