Having worked on this for quite a few years (compute in memory with a variety of emerging memories: RRAM, MRAM others) with a substantial research team, our conclusion ended up being you are better off with SRAM based solutions. And most likely tightly coupled memory with digital compute is better than doing compute in memory.

The newer memories like RRAM are simply not stable enough: too much variations, drift with temperature, reliability etc. On some cases you can try and re engineer the devices to be better suited but they invariably end up being larger, or more power hungry, and often both. See for example https://ieeexplore.ieee.org/document/9405305 (sorry for the paywall - no open access available)

Adding insult to injury, none of these emerging memories can be integrated with highly scaled digital CMOS. (22nm is about a low as you can go for eg MRAM and RRAM - where they are offered as embedded flash alternatives) But you will always need flexible, programmable digital compute in order to have an AI accelerator that can do more than 1 flavor of resnets.

SRAM, in the meantime does scale relatively nicely and co integrates well with digital logic across the whole spectrum down to 5nm FinFETs and below.