Verification with Transfer: Exact Information Frontiers and Their Price in Calls
Theory paper prices source-task calls that cut verification cost, with Lean-checked bounds and a transformer test.
Under a flat prior over k-bit answers, zero-error verification needs 2^k-1 checks. The paper derives an exact information frontier for interleaving source calls with n verifications and shows designed sources nearly meet the expected-call lower bound, within 1+log2(5) calls for unique answers. For linear banks over GF(2), accuracy has a closed form and, after a polynomial reduction, the budget profile is computable in 2^{O(h^2)} poly(J, k+h) time. Nearly all numbered results are machine-checked in Lean 4; a small transformer used all delivered bits at latent dimension 5 and none at 11 under fixed training budgets.
- Zero-error verification of a flat k-bit answer needs 2^k-1 checks
- One pre-verification observation attains the causal information lower bound
- GF(2) bank budgets are computable in 2^{O(h^2)} poly(J, k+h) time
- Lean 4 checks every numbered result except two planner clauses
- A small transformer used delivered bits at latent dimension 5, none at 11
From the original article
1 min read at arxiv.orgA verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications. The usual remedy is to solve related source tasks, either all first, as a curriculum does, or interleaved with verification. We price this remedy in information and in calls.
By Hazar Yueksel · arxiv.org
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