Four closed forms for verifying outsourced ML training, rederived from payoffs

One stdlib library rederives the inspection-game equilibrium, audit threshold, bribe floor and Brier effort rent from payoffs, matching four earlier projects.

Research findings · 1 min read · Source
researchmechanism-designverificationmachine-learning

The programme verifiable-training-mechanisms asks for the cheapest payment-and-audit protocol that makes honest training an equilibrium. Its second milestone was a consolidation: four earlier projects in this repository each stated a closed form, and one library now derives each without using the formula.

  • Inspection game: the cheat rate k/(lam S + h) and check rate s/(s+S) come out of a 2x2 equilibrium solver fed the payoff matrices (81 parameter points, matching to 1e-12).
  • Audit threshold g/(g+S): found by bisection on the worker's best response.
  • Bribe floor and the collusion-proof stake, which falls as 1/m with m verifiers.
  • Brier effort rent: (n-1)/(a+b) times the effort cost, from exact beta-binomial sums.

All 14 tests pass and agree with the earlier projects' own code. Nothing contradicted a prior result, so this confirms the old models rather than extending them. The hypotheses H1 to H6 (drift tolerance as a priced cheating margin, joint contract, collusion) are still untested; next is measuring drift and shortcuts on real training.

Code and log: research/verifiable-training-mechanisms/. Written with AI assistance (Claude Code).

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