When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation
When can additional low-bit residual computation replace missing numerical precision for a fixed input-output map? We model a quantized residual system over a fixed horizon as a pure schedule selecting fields from a declared low-bit operation library, and use relaxed controls to characterize its infinite-depth limit. The distance from the target to the closed relaxed reachable set is the exact structural floor: no increase in depth can remove it for that library. Pure schedules approach the relaxed class at rate $O(D^{-1})$ under bounded-variation time dependence and $O(D^{-\vartheta}+D^{-1})$ under Holder dependence of exponent $\vartheta$. Execution arithmetic can reverse this conclusio...
| Authors | Mojtaba Soltanalian |
|---|---|
| Primary category | cs.LG |
| Published | 25 July 2026 |
| Last updated at source | 25 July 2026 |
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