Verification with Transfer: Exact Information Frontiers and Their Price in Calls
A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications.
Key points
- With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification.
- It lower-bounds the expected number of binary source calls, which designed sources meet within $1+\log25$ calls for unique answers and within a logarithmic term in general, where no additive constant suffices.
- With an exact verifier and fixed sources, moving every call before the first verification preserves all hard caps on calls, although interleaving can save unboundedly many expected calls; under a noisy verifier, source-first protocols can lose unbounded factors in information and in error.
- For linear banks over $\mathbb{F}2$, optimal accuracy has a closed form, and after a polynomial-time reduction the budget profile is computable in time $2^{O(h^2)}\operatorname{poly}(J,k+h)$ for $J$ sources and nuisance dimension $h$.
Sources (1)
- [1]Verification with Transfer: Exact Information Frontiers and Their Price in CallsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 04:00 PM
A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications.
With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification.
Extractive summary: sentences quoted from the sources.