I think you mean inference compute? I believe all expert weights are updated in each backward pass during MoE training. The first benefit was getting a sort of structured pruning of weights through the mechanism of expert selection so that the model didn’t need to go through ‘unnecessary’ parts of the model for a given token. This then let inference use memory more efficiently in memory constrained environments, where non-hot or less common experts could be put into slow RAM, or sometimes even streamed off storage.

But I don’t think it necessarily saved training cost; if it did, I’d be interested to learn how!

MoE models will have far more world knowledge than dense models with the same amount of active parameters. MoE is a no-brainer if your inference setup is ultimately limited by compute or memory throughput - not total memory footprint - or alternately if it has fast, high-bandwidth access to lower-tier storage to fetch cold model weights from on demand.