EnergyCal: Taming Loss Spikes in Muon-Family Optimizers for Sparse MoE Training

Masato Fujitake

Sparse mixture-of-experts (MoE) language-model training can exhibit large loss spikes with Muon-family optimizers. We introduce EnergyCal, a lightweight rule that attenuates routed-expert updates according to the normalized squared Frobenius norm of their finite-step Newton-Schulz directions. EnergyCal leaves the spectral transform unchanged and adds no persistent optimizer state. We evaluate it on a 4B-parameter MoE model. Against a development-selected, lower-learning-rate MuonH recipe, EnergyCal-MuonH reduces mean thresholded loss-spike burden by 99.51% and final geometric-mean perplexity by 4.06%, with a modest throughput cost. With plain Muon at matched nominal learning rate and weight decay, the reduction in mean spike burden averages 95.98% across the two tested exponents, accompanied by small endpoint improvements. These findings support stabilization both with and without Hyperball in the evaluated setting.