Direction-Preserving Number Representations
Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes an...
| Authors | Bardia Zadeh, George A. Constantinides |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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