Simulates loss-spike risk grounded in the 2025 wave of matrix-aware optimizer research. 448 configs across 7 optimizers (naive vs. fixed Muon/SOAP variants, plus Gluon and 8-bit Muon), 4 batch regimes, 4 model scales (0.5B-70B). Ten sources, nine from 2025 and one a July 2026 technical report, in optimizer_stability_theory.py — including "Muon is Scalable for LLM Training" (Moonlight model paper), a formal Muon convergence analysis, and a unified SOAP/Muon/AdamW stability study identifying and fixing SOAP's large-batch loss spikes.
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