Standard low-precision formats are suboptimal for vector direction preservation compared to optimized scalar alphabets and spherical codes, with gaps quantified analytically and proven in Lean, and NVIDIA's E2M1 nearly matching the optimum for 4 bits.
A Short Course on Rearrangement In- equalities
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Direction-Preserving Number Representations
Standard low-precision formats are suboptimal for vector direction preservation compared to optimized scalar alphabets and spherical codes, with gaps quantified analytically and proven in Lean, and NVIDIA's E2M1 nearly matching the optimum for 4 bits.