Agree there are already plenty of incentives to produce more efficient and powerful ai hardware.
With this project, experimenting to design a pow that "forces" miners to also be capable of the same kind of "useful" computation. (and keeping the pow as simple as possible, not specific to particular type of gpu etc, so that future type of hardware good at matmul rounds will even be better at mining, for ex future photonic or analog chips etc specialized for this type of ai compute)

Afaik previously litecoin attempted to prevent asics by using scrypt and being memory bound, to try to keep mining more decentralized, but asics were still developed for it that also serve no other purpose than mining and this contributes to centralization.
Here, trying to make it so that if miners are optimized for this pow, they are necessarily also capable of useful "ai" computation, regardless if using custom asic developed for that pow or not.

In order to achieve this, the pow is computing rounds of (ternary) mat mults, and trying to adjust biases and non-linerarity such that computation is both hard to reverse (trying to ensure hash properties similar to LWE) and useful for ai.
By making it necessary for miners to also be capable of useful work (though not at same time as mining), maybe this can also help prevent decentralization of mining power (like LTC aimed to achieve).