Query-Dependent Reading for Quantized Inner-Product Estimation: A Minimax Separation

Key points

• 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 $x^\top y$.1
• First, we show that query-independent reading cannot benefit from extra storage.1
• We prove the matching lower bound for arbitrary scalar decoders, extending the result for unbiased compressors [Safaryan et al., 2020].1
• We construct a two-batch protocol using Gaussian projections and random thresholds, with asymptotic normalized error at most $(π+o(1))/[4R\log(W/R)]$ as $W/R\to\infty$.1

Sources (1)

• [1]Query-Dependent Reading for Quantized Inner-Product Estimation: A Minimax Separation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 17, 10:12 PM

  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 $x^\top y$.

Extractive summary: sentences quoted from the sources.