When do verifiers complement rather than substitute?

What it found

Exact value of verifier committees for an accept/slash decision: value is zero below a closed-form minimum committee size (4 at π=0.05, q=0.7) even though mutual information is submodular, 24–34% of triples violate diminishing returns, myopic marginal-value hiring buys nothing (ratio 0 to the optimum) and leave-one-out pay is a parity sawtooth that falls 7× below average value at 40 verifiers. Stylised.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Verification games & slashing

• How big should a random verifier committee be?Verifier committees from a finite pool: exact hypergeometric capture (zero once m ≥ 2B+1, up to 26× below binomial), exact size ≈0.90 of ln(1/ε)/KL(½‖β) vs Hoeffding up to 2.2× too large, stake-weighted draws depend only on Byzantine stake share (20 of 100 nodes at 4× stake capture a 41-committee w.p. ½), and the threshold safety/liveness trade-off.
• Are reward pools identity-proof?Identity splitting vs merging under stake-weighted pools: split-invariant iff the weight is linear in stake, per-head optimum √(Rn/c)−n, sharp deterrence fee Rn/((n+1)(n+2)), wagering split-neutral.
• Can a bond tell reliable hardware from unreliable?Can a bond tell reliable hardware from unreliable? Single crossing runs the wrong way: reliable rent (θ_H−θ_L)(c+(1+ρ)s_H)/(1−θ_H) is minimised at zero stake, a flat wage is optimal, and a deterrence stake scales rent by (c+(1+ρ)s)/c.
• How many milestones does an unenforced job need?Milestone payments without enforcement: a split pre-payment needs only the pooled relationship value (C/(W_r+W_w) vs P/W_r, C/W_w), and front-loading makes the milestone count logarithmic, ⌈ln(1+(V−C)/W)/ln(V/C)⌉ (17 vs 100 at W=1).
• What is the cheapest payment-and-audit protocol that makes honest ML training an equilibrium?Research programme: incentive-compatible verification of outsourced ML training; first measurement on real training finds a tolerance-tau referee passes a skip-steps cheat on 30% of steps at tau = 1e-2 while the held-out loss stays within one seed std, and the loss only suffers at tau about 10x the worst benign drift; milestone 4 prices contracts by linear programme: with a tolerance, audit-only cannot enforce full effort and the joint contract beats both checks only when the score is precise (4 of 45 cells); milestone 6: against a coordinating majority replication adds no deterrence beyond the audit and the stake is flat in the number of workers (140 cells); milestone 5: an agreement term between redundant workers is worth nothing beyond the audit once cheats copy one trajectory (0 of 1,349 random instances), and a proved one-sided bound max(C, g/p - S) holds in 2,755 instances but is vacuous for a noisy score
• Economics of refereed verificationInspection-game economics of refereed verification: stake substitutes for re-execution, extra verifiers free-ride, and optimal tolerance/stake under floating-point drift.

All 19 Verification games & slashing projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.