We measure what unbiased stochastic-rounding MXFP4 noise on all four backward GEMM operands (forward pass in BF16) costs Muon at the end of pretraining. The set
In Muon-trained language models the constant-LR population gradient is mostly a period-2 bounce. We measure this and test its consequences for momentum and batc
Hashed n-gram input tables (Over-Encoding) buy prediction with stored parameters instead of FLOPs. We measure how to spend that budget in a 26M-parameter Muon-t