Muon Optimizer's Spectral Space Trick

willdepue · x · 2026-07-14

The author shares a trick for the **Muon optimizer**: rather than hiding image information in the parameter's entry space, it's better to "hide it in the spectral space," as the optimizer updates more gently along its own norm directions. The original post explains that Muon diffuses updates across more gradient directions, making it better at erasing information written directly into the weights. However, it allocates less noise to fixed-direction updates, so encoding information into the spectral space allows it to survive training. The author also mentions that this method showed "very good retention" during the **NanoGPT speedrun**.

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