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Why does a Hadamard rotation make W4A4 quantization work, which rotations run online, and what do they cost?

Rotating a model before quantizing it changes nothing in exact arithmetic and almost everything at 4 bits. The answer shows why with a runnable demo, says which rotations are free and which run on every token, prices the online ones, and names the format that makes the trick unnecessary.

Updated Oct 2026 · Worked answers on inference mechanisms, with calculations, implementation details, and follow-up questions.

Rotating a model before quantizing it changes nothing in exact arithmetic and almost everything at 4 bits. The answer shows why with a runnable demo, says which rotations are free and which run on every token, prices the online ones, and names the format that makes the trick unnecessary.

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