Query-Dependent Reading for Quantized Inner-Product Estimation: A Minimax Separation
We study quantization for inner-product estimation when storage and reading have separate budgets. In the static bit-probe model [Yao, 1981], an encoder stores $w$ bits about $x$ before seeing a query $y$, and a reader probes at most $r<w$ bits to estimate $x^\top y$. Both vectors lie in the $d$-dimensional Euclidean unit ball. Protocols may be randomized, and computation is unrestricted. Performance is measured by $d$ times the worst-case mean-squared error over $x,y$, averaged over protocol randomness. First, we show that query-independent reading cannot benefit from extra storage. Any such reader is equivalent to fully reading an $r$-bit message, even when later reads depend on previou...
| Authors | Krishnakumar Balasubramanian, Siddharth Bhandari, Shiva Prasad Kasiviswanathan |
|---|---|
| Primary category | cs.IT |
| Published | 17 October 2026 |
| Last updated at source | 17 October 2026 |
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