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What is maximal update parameterization (muP), and why...
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See plansUnder standard parameterization, the optimal learning rate migrates predictably as width grows — tune it on a 200M proxy and by 7B the true optimum may have shifted by several times, forcing an expensive re-sweep at every scale you care about. muP fixes this by choosing initialization variance and per-layer learning rates so activation magnitudes and the size of each optimizer step stay order-1 per coordinate regardless of width, not just at initialization but through training. For Adam, that works out to scaling each layer’s learning rate inversely with its fan-in while leaving embeddings at the base rate, and standard Kaiming-style initialization already satisfies the initialization half of the condition.
The payoff: sweep the base learning rate once on a cheap proxy — tens to low hundreds of millions of parameters — and that same base rate, rescaled by the fixed per-layer factor, transfers cleanly to 7B or 70B with no further search, turning a multi-million-GPU-hour re-tune into a near-free upfront cost. It doesn’t make a model better than a perfectly-tuned standard run would be — its value is entirely in making a near-optimal learning rate cheap to find at any scale — and it breaks whenever a new architectural knob introduces a size-dependent magnitude that the existing per-layer correction doesn’t account for.