Physical analog chemical circuits whose physical structure directly is the network, and use chemistry/physics directly for the computations. For example, a sum is usually represented as the number of physical ions present within a space, not some ALU that takes in two binary numbers, each with some large number of bits, requiring shifting electrons to and from buckets, with a bunch of clocked logic operations.
There are a few companies working on more "direct" implementations of inference, like Etched AI [1] and IBM [2], for massive power savings.
[1] https://en.wikipedia.org/wiki/Etched_(company)
[2] https://spectrum.ieee.org/neuromorphic-computing-ibm-northpo...
My armchair take would be that watt usage probably isn't a good proxy for computational complexity in biological systems. A good piece of evidence for this is from the C. elegans research that has found that the configuration of ions within a neuron--not just the electrical charge on the membrane--record computationally-relevant information about a stimulus. There are probably many more hacks like this that allow the brain to handle enormous complexity without it showing up in our measurements of its power consumption.
Jaxley: Differentiable simulation enables large-scale training of detailed biophysical models of neural dynamics [1]
They basically created sofware to simulate real neurons and ran some realistic models to replicate typical AI learning tasks:
"The model had nine different channels in the apical and basal dendrite, the soma, and the axon [39], with a total of 19 free parameters, including maximal channel conductances and dynamics of the calcium pumps."
So yeah, real neurons are a bit more complex then ReLU or Sigmoid.
[1] https://www.biorxiv.org/content/10.1101/2024.08.21.608979v2....
That said, I think there is a good reason to be skeptical that it is a good chance. The consistent trend of finding higher complexity than expected in biological intelligences (like in C. Elegans), combined with the fact that the physical nature of digital architectures versus biological architectures are very different, is a good reason to bet on it being really complex to emulate with our current computing systems.
Obviously there is a way to do it physically--biological systems are physical after all--but we just don't understand enough to have the grounds to say it is "likely" doable digitally. Stuff like the Universal Approximation Theorem implies that in theory it may be possible, but that doesn't say anything about whether it is feasible. Same thing with Turing completeness too. All that these theorems say is our digital hardware can emulate anything that is a step-by-step process (computation), but not how challenging it is to emulate it or even that it is realistic to do so. It could turn out that something like human mind emulation is possible but it would take longer than the age of the universe to do it. Far simpler problems turn out to have similar issues (like calculating the optimal Go move without heuristics).
This is all to say that there could be plenty of smart ideas out there that break our current understandings in all sorts of ways. Which way the cards will land isn't really predictable, so all we can do is point to things that suggest skepticism, in one direction or another.