Where Should Optimizer State Live? Tiered State Allocation for Memory-Efficient Mixture-of-Experts Training

Optimizer state is the largest single line item in the memory budget of mixture-of-experts (MoE) training: on a 6.78B-parameter MoE language model, AdamW keeps 50.6 GB of first and second moments to update 12.6 GB of bfloat16 weights. We study SkewAdam, an optimizer built on the observation that the three parameter populations of an MoE - the dense backbone, the experts, and the router - differ enough in size and gradient statistics that they should not receive the same state. SkewAdam keeps float32 momentum plus a factored second moment for the backbone (5% of parameters), a factored second moment alone for the experts (95%), and an exact second moment for the router (