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Introduces Variable Bit-width Quantization (VBQ), a training-time method where each group of 64 weights learns its own bit-width (1,2,4,8) via Gumbel-Softmax relaxation. VBQ discovers a heterogeneous allocation that yields a 'bigger-but-smaller' regime, e.g., a 131M parameter model at 1.82 mean bits beats a 55M FP16 model while using less storage, and a 1.46B model matches a 593M FP16 with ~3.7x less storage.